Department of Physics

Rachel Mandelbaum, Interim Department Head
Location: Wean Hall 7325

Gillian Lynn Ryan, Director of Undergraduate Affairs
Location: Wean Hall 7303

Hanann Marawi, Academic Program Manager
Location: Wean Hall 7319
www.cmu.edu/physics

Physics, one of the basic sciences, has its origin in the irrepressible human curiosity to explore and understand the natural world. This fundamental urge to discover has led to the detailed understanding of a remarkable variety of physical phenomena. Our knowledge now encompasses the large-scale movement of galaxies, the minute motions within atoms and nuclei, and the complex structure of the assemblies of molecules that make life possible. The spectacular expansion of our comprehension of the physical world forms an impressive part of the intellectual and cultural heritage of our times. The opportunity to add to this heritage is an important source of motivation for young physicists. The application of discoveries in physics to the solution of complex modern technological problems offers a vast field in which physicists make decisive contributions. The interplay of pure and applied physics has always been fruitful and today ensures many rewarding career opportunities for physics students. The deep understanding of the physical world developed by physics majors prepares them for success in a wide variety of careers well beyond physics, from medicine to all the sciences and engineering.

Carnegie Mellon’s undergraduate curriculum in physics has been carefully designed to provide a firm knowledge of the basic principles of physics, an appreciation of a wide range of physical problems of current interest, and the capacity to formulate and solve new problems. In addition to classwork and problem solving, the curriculum includes studying physical phenomena in the laboratory. Physics students are strongly encouraged to go beyond the formal theoretical and experimental course work and become involved in research projects under the guidance of individual faculty members.

Students may choose from a variety of degree options. The objectives and requirements for each of these options are described below. Each allows considerable latitude in the choice of electives:

B.S. in Physics
B.A. in Physics
B.S. in Physics with Tracks in:
- Applied Physics
- Astrophysics
- Biological Physics
- Chemical Physics
- Computational Physics
- Quantum Physics
Minor in Physics

Students pursuing a B.S. in Physics, with any track, will take all courses from the Physics, Mathematics, and Technical Core lists, and take an appropriate selection of courses from the Technical, Non-Technical, Physics Breadth, and Qualifying Physics Elective lists. These lists are detailed below.

Through the judicious choice of elective courses, a double major program combining physics and another discipline can be readily achieved. A minor in physics is also offered for those students who major in other disciplines. The student, with the help of their faculty advisors, can easily build a program that aims at specific career objectives.

The Department maintains an active and wide-ranging program of advising. Beyond aiding in academic planning, the Director of Undergraduate Affairs can also assist students in finding research work during the academic year, technical jobs and internships for the summer, as well as planning and executing the necessary steps for gaining employment or continuing their studies beyond the bachelor’s degree. Whether students follow a standard curriculum or not, they should consult their academic advisor at least once every semester.

Sample Schedule for a B.S. in Physics

B.S. in Physics

B.S. degree candidates can choose studies in not only a wide variety of intermediate and advanced topics in physics but also a range of material in other science or engineering fields. The B.S. degree provides a solid foundation for students wishing to go on to graduate work in physics or any of a large number of fields in pure or applied science or engineering for which a sound grasp of physics and mathematics is essential. This program also provides excellent preparation for careers in teaching, for work in industrial or governmental research and development, or for other employment in business or industry with a significant scientific component.

Degree Requirements

Physics Core:

All physics majors take these courses in physics, which are designed to teach the fundamentals required for any specialty. Many students take the 100-level courses in their first year of study, the 200-level courses in their second year, and the 300-level courses in their third or fourth year.

		Units
33-121	Physics I for Science Students	12
or 33-151	Matter and Interactions I
Corequisite for 33-121 is 21-120
33-142	Physics II for Engineering and Physics Students	12
or 33-152	Matter and Interactions II
33-104	Experimental Physics	9
33-201	Physics Sophomore Colloquium I	2
33-211	Physics III: Modern Essentials	10
33-231	Physical Analysis	10
33-202	Physics Sophomore Colloquium II	2
33-228	Electronics I	10
33-232	Mathematical Methods of Physics	10
33-234	Quantum Physics	10
33-301	Physics Upperclass Colloquium I	1
33-331	Physical Mechanics I	10
33-338	Intermediate Electricity and Magnetism I	10
33-341	Thermal Physics I	10
33-302	Physics Upperclass Colloquium II	1
33-340	Modern Physics Laboratory	10
Total Physics Core Units		129

Mathematics Core:

All physics majors take these calculus courses from the Department of Mathematics to support their studies in physics.

		Units
21-120	Differential and Integral Calculus	10
21-122	Integration and Approximation	10
21-259	Calculus in Three Dimensions	10
Total Mathematics Core Units		30

Technical Core:

All students in the Mellon College of Science take courses in the Life Sciences, Physical Sciences, and Mathematics, Statistics, or Computer Science to gain the technical breadth necessary for interdisciplinary work. The following three courses have been selected specifically for physics majors to give them the technical breadth they need.

		Units
03-121	Modern Biology ¹	9
09-105	Introduction to Modern Chemistry I ²	10
15-110	Principles of Computing ³	10-12
or 15-112	Fundamentals of Programming and Computer Science

Total Technical Core Units		29-31

_{[1] If 03-121 is satisfied through placement credit, students should refer to the Mellon College of Science’s Life Sciences list to fulfill technical breadth requirement A.}

_{[2] If 09-105 is satisfied through placement credit, students should refer to the Mellon College of Science’s Physical Sciences list to fulfill technical breadth requirement B.}

_{[3] If 15-112 is satisfied through placement credit, students should refer to the Mellon College of Science’s STEM Course list to fulfill technical breadth requirement D.}

Technical Electives:

Physics majors can choose to increase the breadth or depth of their studies through their choices of Technical Electives. Students may choose these electives individually or may take a pre-set selection of technical electives known as a “track” to focus on a specific subfield of physics. The six available tracks are detailed here.

		Units
33-xxx	Physics Breadth Elective	9-12
33-xxx	Three Qualifying Physics Electives	27-36
21-2xx	Mathematics Elective	9-10
xx-xxx	Three STEM Electives ⁴	27-36
Total Technical Electives Units		72-94

_{[4] STEM electives are any courses in MCS (including Physics), SCS, Statistics, CIT, and others explicitly approved by the Director of Undergraduate Affairs.}

Non-Technical Electives:

The Mellon College of Science requires that all students take a variety of non-technical courses to strengthen their understanding of both themselves and the world at large.

		Units
99-101	Core@CMU	3
76-101	Interpretation and Argument	9
38-101	EUREKA!: Discovery and Its Impact	6
38-110	ENGAGE in Service	1
38-220	ENGAGE in the Arts	2
38-230	ENGAGE in Wellness: Looking Inward	1
38-330	ENGAGE in Wellness: Looking Outward	1
38-430	ENGAGE in Wellness: Looking Forward	1
38-304	Reading and Writing Science ⁵	6
xx-xxx	Cultural/Global Understanding Elective ⁶	9
xx-xxx	Four Non-Technical Electives ⁷	36
Total Non-Technical Units		75

_{[5] Refer to the Mellon College of Science’s Science and Society list for alternate courses that will fulfill this requirement. Placement credit may not be used.}

_{[6] Refer to the Mellon College of Science’s Cultural/Global Understanding list for courses that will fulfill this requirement. Placement credit may not be used.}

_{[7] Refer to the Mellon College of Science’s Arts, Humanities, and Social Sciences section for courses that will fulfill the non-technical electives requirement. Up to 18 units may be fulfilled through placement credit.}

Free Electives:

All students must complete a minimum of 360 units to earn a bachelor’s degree in the Mellon College of Science. Students are welcome to take more than the minimum 360 units required.

		Units
xx-xxx	Free Electives ⁸	1-26
Total Free Elective Units		1-26

_{[8] A maximum of 9 units of physical education and/or military science and/or STUCO courses may be taken as free electives.}

Sample Schedule (No Track)

BEGINNING FALL 2015 AND BEYOND

First Year

Fall		Units
99-101	Core@CMU	3
38-101	EUREKA!: Discovery and Its Impact	6
33-121	Physics I for Science Students	12
or 33-151	Matter and Interactions I
Corequisite for 33-121 is 21-120 & for 33-151 is 21-122
21-120	Differential and Integral Calculus	10
or 21-122	Integration and Approximation
xx-xxx	MCS/Physics Technical Core Requirement 1 of 3	9-12
76-101	Interpretation and Argument	9
or 76-100	Reading and Writing in an Academic Context
First-Year Fall Units		49-52

Spring		Units
33-142	Physics II for Engineering and Physics Students	12
or 33-152	Matter and Interactions II
Corequisite for 33-142 is 21-122 & for 33-152 is 21-259
33-104	Experimental Physics	9
21-122	Integration and Approximation	10
or 21-259	Calculus in Three Dimensions
xx-xxx	MCS/Physics Technical Core Requirement 2 of 3	9-12
xx-xxx	Non-Technical Elective 1 of 4	9
First-Year Spring Units		49-52

Sophomore Year

Fall		Units
33-201	Physics Sophomore Colloquium I	2
33-211	Physics III: Modern Essentials	10
33-231	Physical Analysis	10
21-259	Calculus in Three Dimensions (if not already taken)	10
xx-xxx	MCS/Physics Technical Core Requirement 3 of 3	9-12
xx-xxx	Cultural/Global Understanding Elective	9-12
Sophomore Fall Units		50-56

Spring		Units
38-230	ENGAGE in Wellness: Looking Inward	1
33-202	Physics Sophomore Colloquium II	2
33-228	Electronics I	10
33-232	Mathematical Methods of Physics	10
33-234	Quantum Physics	10
xx-xxx	Technical Elective 1 of 8	9-12
Sophomore Spring Units		42-45

Junior Year

Fall		Units
38-330	ENGAGE in Wellness: Looking Outward	1
33-301	Physics Upperclass Colloquium I	1
33-331	Physical Mechanics I	10
33-338	Intermediate Electricity and Magnetism I	10
33-341	Thermal Physics I	10
xx-xxx	Technical Elective 2 of 8	9-12
Junior Fall Units		41-44

Spring		Units
33-302	Physics Upperclass Colloquium II	1
38-304	Reading and Writing Science (Science and Society)	6
33-340	Modern Physics Laboratory	10
38-110	ENGAGE in Service	1
xx-xxx	Technical Elective 3 of 8	9-12
xx-xxx	Technical Elective 4 of 8	9-12
xx-xxx	Non-Technical Elective 2 of 4	9-12
Junior Spring Units		45-54

Senior Year

Fall		Units
38-430	ENGAGE in Wellness: Looking Forward	1
38-220	ENGAGE in the Arts	2
xx-xxx	Technical Elective 5 of 8	9-12
xx-xxx	Technical Elective 6 of 8	9-12
xx-xxx	Non-Technical Elective 3 of 4	9-12
xx-xxx	Free Elective	9-12
xx-xxx	Free Elective	9-12
Senior Fall Units		48-63

Spring		Units
xx-xxx	Technical Elective 7 of 8	9-12
xx-xxx	Technical Elective 8 of 8	9-12
xx-xxx	Non-Technical Elective 4 of 4	9-12
xx-xxx	Free Elective	9-12
Senior Spring Units		36-48

B.A. in Physics

The Bachelor of Arts degree in Physics offers a flexible program that allows students to combine the study of Physics with the opportunity to do intensive work in substantive areas such as liberal arts, teaching, business or law. With up to 80 units of free electives, it is feasible for students to obtain, for example, an additional major with a department in the Dietrich College of Humanities and Social Sciences, the College of Fine Arts, or the Tepper School of Business. It is expected that students will focus their elective courses in a well-defined academic area. Students must meet with the Director of Undergraduate Affairs and construct an approved plan of study.

The requirements for the B.A. degree are the same as for the B.S. degree, except that 6 of the Physics, Mathematics and Technical Electives in the B.S. program become Free Electives in the BA program. These requirements are listed below.

Degree Requirements

Physics Core:

		Units
33-121	Physics I for Science Students	12
or 33-151	Matter and Interactions I
Corequisite for 33-121 is 21-120
33-142	Physics II for Engineering and Physics Students	12
or 33-152	Matter and Interactions II
Corequisite for 33-142 is 21-122
33-104	Experimental Physics	9
33-201	Physics Sophomore Colloquium I	2
33-211	Physics III: Modern Essentials	10
33-231	Physical Analysis	10
33-202	Physics Sophomore Colloquium II	2
33-228	Electronics I	10
33-232	Mathematical Methods of Physics	10
33-234	Quantum Physics	10
33-301	Physics Upperclass Colloquium I	1
33-331	Physical Mechanics I	10
33-338	Intermediate Electricity and Magnetism I	10
33-341	Thermal Physics I	10
33-302	Physics Upperclass Colloquium II	1
33-340	Modern Physics Laboratory	10
Total Physics Core Units		129

Mathematics Core:

All Physics Majors take these courses from the Department of Mathematics to support their studies in Physics.

		Units
21-120	Differential and Integral Calculus	10
21-122	Integration and Approximation	10
21-259	Calculus in Three Dimensions	10
Total Mathematics Core Units		30

Technical Core:

All students in the Mellon College of Science take courses in the Life Sciences, Physical Sciences, and Mathematics, Statistics, or Computer Science to gain the technical breadth necessary for interdisciplinary work. These three courses have been selected specifically for Physics Majors to give them the technical breadth they need

		Units
03-121	Modern Biology ⁹	9
09-105	Introduction to Modern Chemistry I ¹⁰	10
15-112	Fundamentals of Programming and Computer Science ¹¹	10-12
or 15-110	Principles of Computing
Total Technical Core Units		29-31

_{[9] If 03-121 is satisfied through placement credit, students should refer to the Mellon College of Science’s Life Sciences list to fulfill technical breadth requirement A.}

_{[10] If 09-105 is satisfied through placement credit, students should refer to the Mellon College of Science’s Physical Sciences list to fulfill technical breadth requirement B.}

_{[11] If 15-112 is satisfied through placement credit, students should refer to the Mellon College of Science’s STEM Course list to fulfill technical breadth requirement D.}

Technical Electives:

While students pursuing a B.S. in Physics are required to take a minimum of 8 Physics, Mathematics, and STEM electives, students pursuing a B.A. in Physics need only take a minimum of 2 Qualifying Physics Electives.

		Units
33-xxx	Two Qualifying Physics Electives	18-24
Total Technical Electives		18-24

Non-Technical Electives:

The Mellon College of Science requires that all students take a variety of non-technical courses to strengthen their understanding of both themselves and the world at large. The precise requirements are different for those entering before and after the Fall of 2015.

		Units
99-101	Core@CMU	3
76-101	Interpretation and Argument	9
38-101	EUREKA!: Discovery and Its Impact	6
38-110	ENGAGE in Service	1
38-220	ENGAGE in the Arts	2
38-230	ENGAGE in Wellness: Looking Inward	1
38-330	ENGAGE in Wellness: Looking Outward	1
38-304	Reading and Writing Science ¹²	6
38-430	ENGAGE in Wellness: Looking Forward	1
xx-xxx	Cultural/Global Understanding Elective ¹³	9
xx-xxx	Four Non-Technical Electives ¹⁴	36
Total Non-Technical Elective Units		75

_{[12] Refer to the Mellon College of Science’s Science and Society list for alternate courses that will fulfill this requirement. Placement credit may not be used.}

_{[13] Refer to the Mellon College of Science’s Cultural/Global Understanding list for courses that will fulfill this requirement. Placement credit may not be used.}

_{[14] Refer to the Mellon College of Science’s Arts, Humanities, and Social Sciences section for courses that will fulfill the non-technical electives requirement. Up to 18 units may be fulfilled through placement credit.}

Free Electives:

All students must complete a minimum of 360 units to earn a bachelor’s degree in the Mellon College of Science. Students are welcome to take more than the minimum 360 units required. The B.A. in Physics replaces 6 Technical Electives with Free Electives, compared to the B.S. in Physics.

		Units
xx-xxx	Free Electives ¹⁵	72-80
Total Free Electives		72-80

_{[15] A maximum of 9 units of physical education and/or military science and/or StuCo courses may be taken as free electives.}

Physics Electives

Physics Breadth Electives

Students pursuing a B.S. in Physics must take at least one course from the Physics Breadth Elective list to gain experience in a subfield of physics. Some tracks have this course prescribed, while others allow free choice from this list. All of these courses may also be taken as Qualifying Physics Electives, but they may not fulfill both requirements simultaneously.

		Units
33-224	Stars, Galaxies and the Universe	9
33-226	Physics of Energy	9
33-353	Intermediate Optics	12
33-355	Nanoscience and Nanotechnology	9
33-441	Introduction to Biophysics	10
33-444	Introduction to Nuclear and Particle Physics	9
33-448	Introduction to Solid State Physics	9
33-466	Extragalactic Astrophysics and Cosmology	9
33-467	Astrophysics of Stars and the Galaxy	9
33-650	General Relativity	9

Total Physics Breadth Elective Units9-12

Qualifying Physics Electives

Students pursuing a B.S. in Physics must take at least three courses totaling at least 27 units from the Qualifying Physics Elective list, not including the 100-level courses. Some tracks have these courses prescribed, while others allow free choice from this list, enabling students to choose between broad and in-depth study. Students pursuing a B.A. in Physics must take at least two courses totaling at least 18 units from this list. Students pursuing a Minor in Physics must take at least three courses totaling at least 27 units from this list or non-prescribed courses from the Physics Core list. While all courses on the Physics Breadth Elective list are also on the Qualifying Physics Elective list, a course may not fulfill both requirements simultaneously. Certain courses are offered only in alternate years, as indicated.

33-114	Physics of Musical Sound (B.A. and Minor only) ¹⁶	9
33-115	Physics for Future Presidents (B.A. and Minor only) ¹⁶	9
33-120	Science and Science Fiction (B.A. and Minor only) ¹⁶	9
33-224	Stars, Galaxies and the Universe	9
33-226	Physics of Energy	9
33-241	Introduction to Computational Physics	9
33-332	Physical Mechanics II	10
33-339	Intermediate Electricity and Magnetism II	10
33-342	Thermal Physics II	10
33-350	Undergraduate Research ¹⁷	Var.
33-353	Intermediate Optics (Alt. Fall - F22, F24)	12
33-355	Nanoscience and Nanotechnology (Alt. Fall - F23, F25)	9
33-441	Introduction to Biophysics	10
33-444	Introduction to Nuclear and Particle Physics	9
33-445	Advanced Quantum Physics I	9
33-446	Advanced Quantum Physics II	9
33-448	Introduction to Solid State Physics	9
33-451	Senior Research ¹⁷	Var.
33-456	Advanced Computational Physics	9
33-466	Extragalactic Astrophysics and Cosmology	9
33-467	Astrophysics of Stars and the Galaxy	9
33-499	Supervised Reading ¹⁷	Var.
33-650	General Relativity	9
33-658	Quantum Computation and Quantum Information Theory	10
33-659	Quantum Hall Effect and Topological Insulators	12
33-7xx	Physics Graduate Level Courses (see list below)

Total Qualifying Physics Electives Units27-37

_{[16] Only one of these three courses (33-114, 33-115, and 33-120) may be used for the B.A. These classes may not be used as Qualifying Physics Electives for the B.S.}

_{[17] Only one of these three courses (33-350, 33-451, and 33-499) of 9 units may be used as a Qualifying Physics Elective. Any exceptions must be approved by the Director of Undergraduate Affairs.}

Qualifying Physics Electives Recommended for Physics Graduate School

Students planning to undertake graduate studies in physics are strongly advised to take the following courses, which may count as Qualifying Physics Electives and STEM Electives.

		Units
33-332	Physical Mechanics II	10
33-339	Intermediate Electricity and Magnetism II	10
33-445	Advanced Quantum Physics I	9
33-446	Advanced Quantum Physics II	9

Qualifying Physics Electives Recommended for Graduate Schoolin Physics

Physics Graduate Courses

These courses are intended for graduate students in physics, but may be taken by advanced undergraduates as Qualifying Physics or STEM Electives. Undergraduate students require special permission of the instructor and the Director of Undergraduate Affairs to register for these classes.

		Units
33-755	Quantum Mechanics I	12
33-756	Quantum Mechanics II	12
33-758	Quantum Computation and Quantum Information Theory	12
33-759	Introduction to Mathematical Physics I	12
33-761	Classical Electrodynamics I	12
33-762	Classical Electrodynamics II	12
33-765	Statistical Mechanics	12
33-767	Biophysics: From Basic Concepts to Current Research	12
33-769	Quantum Mechanics III: Many Body and Relativistic Systems	12
33-770	Field Theory I	12
33-771	Field Theory II	12
33-777	Introductory Astrophysics	12
33-778	Introduction to Cosmology	12
33-779	Introduction to Nuclear and Particle Physics	12
33-780	Nuclear and Particle Physics II	12
33-783	Solid State Physics	12

Physics Graduate Course UnitsOptional

Tracks for B.S. in Physics

Students seeking a B.S. in Physics may choose from 5 different Physics tracks, or opt to pursue no track. Each of these tracks fulfills the Technical Electives of the B.S. in Physics. The available tracks are:

No Track
Applied Physics
Astrophysics
Biological Physics
Chemical Physics
Computational Physics
Quantum Physics

The track descriptions and requirements are listed below.

No Track

Physics students wanting maximum freedom can opt not to select a track. The required Technical Electives are those described in the B.S. in Physics section above, and are reprinted below.

		Units
33-xxx	Physics Breadth Elective	9-12
33-xxx	Three Qualifying Physics Electives	27-37
21-2xx	Mathematics Elective	9-10
xx-xxx	Three STEM Electives ¹⁸	27-36
Total Technical Elective Units		72-95

_{[18] STEM electives are any courses in MCS (including Physics), SCS, Statistics, CIT, and others explicitly approved by the Director of Undergraduate Affairs.}

Applied Physics Track

The B.S. in Physics/Applied Physics Track is designed primarily for students who want to prepare for a career path that takes advantage of the diverse and expanding opportunities for employment in industrial and government laboratories with a B.S. degree. The program provides a solid foundation in the concepts of physics, as well as giving the student the experience and understanding of the application of these concepts. The track is intended to enhance computing and laboratory skills, and to introduce the application of physics to those subjects of particular interest to the student. Since the possible subject areas for study are so varied, the track will be tailored to each student’s needs within the framework described below.

		Units
33-448	Introduction to Solid State Physics	9
xx-xxx	Computational Science Course ¹⁹	9-12
xx-xxx	Four Applied Physics/Laboratory Electives ¹⁹	36-48
33-350	Undergraduate Research ¹⁹	9
or 33-451	Senior Research
21-2xx	Mathematics Elective	9-10
Total Applied Track Elective Units		72-88

_{[19] The elective courses and research topic are decided after consultation with, and approval by, the Director of Undergraduate Affairs. Research must be completed in a single 9-unit block.}

Astrophysics Track

The B.S. in Physics/Astrophysics Track provides an option for those Physics majors who either want to specialize in this subfield or plan careers in astronomy or astrophysics. Career paths may include postgraduate training in astronomy or astrophysics or proceeding directly to jobs in these fields. The program provides a thorough foundation in the core physics program with electives concentrating in astrophysics.

		Units
33-224	Stars, Galaxies and the Universe	9
33-466	Extragalactic Astrophysics and Cosmology	9
33-467	Astrophysics of Stars and the Galaxy	9
33-350	Undergraduate Research ²⁰	9
or 33-451	Senior Research
21-2xx	Mathematics Elective	9-10
xx-xxx	Three STEM Electives	27-36
Total Astrophysics Track Elective Units		72-82

_{[20] The research topic must be approved by the Director of Undergraduate Affairs and must be completed in a single 9-unit block.}

Biological Physics Track

The B.S. in Physics/Biological Physics Track combines a rigorous foundation in undergraduate physics with courses in Biological Physics and Chemistry. It is particularly suitable for students preparing for post-baccalaureate careers in the expanding areas of biological and medical physics or for graduate study in biophysics. The program is sufficiently flexible that it can be readily adapted to the requirements of individual students. The student will first meet with the Director of Undergraduate Affairs to discuss interests and career goals and then choose electives that fulfill the requirements of the track.

The Biological Physics Track is excellent preparation for Medical School. All courses suggested for medical school applicants can be completed within this track. Students interested in both the Biological Physics Track and the pre-medical program should consult with both the Director of Undergraduate Affairs in the Physics Department and the Director of the Health Professions Program for help in planning their programs.

Program optimized for Biological Physical studies:

		Units
33-441	Introduction to Biophysics	10
or 03-439	Introduction to Biophysics
33-xxx	One Qualifying Physics Elective	9-12
21-2xx	Mathematics Elective	9-10
03-231	Honors Biochemistry	9
09-217	Organic Chemistry I	9
09-218	Organic Chemistry II	9
03-xxx	Two Biological Sciences Electives ²¹	18
Total Biological Physics Track Elective Units		73-77

_{[21] The elective courses in Biological Sciences are decided after consultation with, and approval by, the Director of Undergraduate Affairs.}

Program optimized for Medical School preparation:

		Units
03-121	Modern Biology	9
or 03-151	Honors Modern Biology
42-202	Physiology	9
03-124	Modern Biology Laboratory	9
or 03-206	Biomedical Engineering Laboratory
or 03-343	Experimental Techniques in Molecular Biology
09-105	Introduction to Modern Chemistry I	10
or 09-107	Honors Chemistry: Fundamentals, Concepts and Applications
09-106	Modern Chemistry II	10
or 09-221	Laboratory I: Introduction to Chemical Analysis
09-207	Techniques in Quantitative Analysis	9
or 09-221	Laboratory I: Introduction to Chemical Analysis
09-217	Organic Chemistry I	9
or 09-219	Modern Organic Chemistry
09-218	Organic Chemistry II	9
or 09-220	Modern Organic Chemistry II
09-208	Techniques for Organic Synthesis and Analysis	9
or 09-222	Laboratory II: Organic Synthesis and Analysis
33-121	Physics I for Science Students	12
or 33-141	Physics I for Engineering Students
Corequisite for 33-121 is 21-120
33-122	Physics II for Biological Sciences & Chemistry Students	9
or 33-142	Physics II for Engineering and Physics Students
Corequisite for 33-122 is 21-122
33-104	Experimental Physics	9
03-231	Honors Biochemistry	9
or 03-232	Biochemistry I
21-111	Calculus I	10
or 21-120	Differential and Integral Calculus
21-112	Calculus II (A semester of statistics may substitute for a semester of calculus at many medical schools.) ¹⁴	10
or 21-122	Integration and Approximation
or 21-124	Calculus II for Biologists and Chemists
36-200	Reasoning with Data	9
or 36-202	Methods for Statistics & Data Science
or
76-101	Interpretation and Argument	9
76-xxx	English II Elective	9
85-xxx	Psychology Elective ^{(Intro to Psychology, Social Psychology)}	9
xx-xxx	Intro to Sociology ^{(not offered at CMU)}	9
Total Biological Physics Track Elective Units		187

Chemical Physics Track

The B.S. in Physics/Chemical Physics Track is designed for students wishing to have a strong grounding in physics along with a specialization in physical chemistry and/or chemical physics. It is particularly suitable for those students planning on graduate studies in physics with an emphasis on chemical physics or chemistry. The program is sufficiently flexible that it can be readily adapted to the requirements of individual students. The student will first meet with the Director of Undergraduate Affairs to discuss interests and career goals and then choose electives that fulfill the requirements of the track.

		Units
33-xxx	One Physics Breadth Elective	9-12
21-2xx	Mathematics Elective	9-10
09-106	Modern Chemistry II	10
09-344	Physical Chemistry (Quantum): Microscopic Principles of Physical Chemistry	9
09-345	Physical Chemistry (Thermo): Macroscopic Principles of Physical Chemistry	9
09-xxx	Three Chemistry Electives ²²	27
Total Chemical Physics Track Elective Units		73-77

_{[22] The elective courses in Chemistry are decided after consultation with, and approval by, the Director of Undergraduate Affairs.}

Computational Physics Track

The B.S. in Physics/Computational Physics Track is intended to fill the increasing demand for physics graduates who are skilled in computational and numerical techniques that are used in the analysis of physical problems in areas ranging from academia to Silicon Valley. The degree provides the student with a rigorous grounding in physics as well as in the foundations and practice of computational skills to address theoretical and applied problems in society. Flexibility in the degree requirements allows students to choose technical electives that prepare them for future careers in a range of emerging computational science fields including data science, artificial intelligence, and software development. Students who complete this track will also gain experience in the application of high-performance computing resources to a wide variety of problems.

		Units
33-241	Introduction to Computational Physics	9
33-456	Advanced Computational Physics	9
33-xxx	One Physics Breadth Elective	9-12
33-xxx	One Qualifying Physics Elective or xx-xxx Computational Science Elective ²³	9-12
21-127	Concepts of Mathematics	12
21-369	Numerical Methods	9-12
or 21-325	Probability
or 36-225	Introduction to Probability Theory
15-122	Principles of Imperative Computation	12
15-150	Principles of Functional Programming	12
Total Computational Physics Track Elective Units		81-90

_{[23] Selected in consultation with, and requires approval of, the Director of Undergraduate Affairs. Common choices outside qualifying physics electives include 10-301, 11-485, and 15-388, but other options may be approved.}

Quantum Physics Track

In the early 20th century, the first quantum revolution led to a disruption of accepted physics paradigms and resulted in rapid innovation in science and technology. The development of the transistor, the laser, and the atomic clock, for example, allowed for innovations in computing, communications, and medical imaging that we now take for granted. The second quantum revolution, defined by the development and application of quantum materials and quantum computing, is poised to unleash another era of innovation in science and technology. The B.S. in Physics/Quantum Physics Track is designed for students who want to prepare for a career at the cutting-edge of this exciting field.

		Units
33-445	Advanced Quantum Physics I	9
33-446	Advanced Quantum Physics II	9
33-658	Quantum Computation and Quantum Information Theory	10
33-448	Introduction to Solid State Physics	9
or 33-444	Introduction to Nuclear and Particle Physics
or 33-355	Nanoscience and Nanotechnology
33-350	Undergraduate Research ²⁴	9
or 33-451	Senior Research
21-2xx	Mathematics Elective	9-10
xx-xxx	Two STEM Electives	18-24
Total Quantum Track Elective Units		73-80

_{[24] The elective courses and research topic are decided after consultation with, and approval by, the Director of Undergraduate Affairs. Research must be completed in a single 9-unit block.}

Additional Major or Dual Degree in Physics

Physics may be taken as an additional major (also known as a “double major”) or as a second degree, with another department granting the primary degree. The rules of the Physics Department for these two options are distinct, as discussed below. Students interested in either option should contact Dr. Gillian Ryan, Director of Undergraduate Affairs, for assistance, and should have successfully completed at least one core physics course at Carnegie Mellon prior to applying for these options.

Additional Major

In order to receive an Additional Major in Physics, with another department granting the primary degree — with a B.S. or B.A., alone or with any track — all requirements of the Physics degree and the particular physics track, as listed in the previous sections, must be fulfilled except:

No STEM Electives are required
No Non-Technical Electives are required
03-121 Modern Biology is not required
09-105 Introduction to Modern Chemistry I is not required
No Free Electives are required

The full requirements are described below:

Physics Core:

		Units
33-121	Physics I for Science Students	12
or 33-151	Matter and Interactions I
Corequisite for 33-121 is 21-120
33-142	Physics II for Engineering and Physics Students	12
or 33-152	Matter and Interactions II
33-104	Experimental Physics	9
33-201	Physics Sophomore Colloquium I	2
33-211	Physics III: Modern Essentials	10
33-231	Physical Analysis	10
33-202	Physics Sophomore Colloquium II	2
33-228	Electronics I	10
33-232	Mathematical Methods of Physics	10
33-234	Quantum Physics	10
33-301	Physics Upperclass Colloquium I	1
33-331	Physical Mechanics I	10
33-338	Intermediate Electricity and Magnetism I	10
33-341	Thermal Physics I	10
33-302	Physics Upperclass Colloquium II	1
33-340	Modern Physics Laboratory	10
Total Physics Core Units		129

Mathematics Core:

All physics majors take these calculus courses from the Department of Mathematics to support their studies in physics.

		Units
21-120	Differential and Integral Calculus	10
21-122	Integration and Approximation	10
21-259	Calculus in Three Dimensions	10
Total Mathematics Core Units		30

Technical Core for an Additional Major:

Students pursuing an additional major in physics do not need to fulfill the full Technical Core required by the Mellon College of Science, but are still required to take either 15-110 or 15-112 (or an equivalent course as pre-approved by the Associate Dean of Undergraduate Affairs, Mellon College of Science).

		Units
15-110	Principles of Computing	10-12
or 15-112	Fundamentals of Programming and Computer Science
Total Technical Core Units		10-12

Technical Electives for an Additional Major:

Students pursuing an additional major in physics must take the Physics Electives and Mathematics Elective required of physics as the primary major, but do not need to take the STEM electives. Students may choose these electives individually, but may opt to complete the requirements as part of the Physics Tracks described in the B.S. in Physics section. Students interested in completing an additional major with a track should consult with the Director of Undergraduate Affairs.

		Units
33-xxx	Physics Breadth Elective	9-12
33-xxx	3 Qualifying Physics Electives	27-37
21-2xx	Mathematics Elective	9-10
Total Technical Electives		45-59

Dual Degree

In order to receive a Dual Degree in another subject and Physics, all requirements of the Physics degree must be fulfilled. Students may choose to complete the B.A. or the B.S. in Physics, with or without a track. Students must complete both the technical and non-technical requirements, and should consult with the Director of Undergraduate Affairs for questions about double counting. The number of units required is 90 more than the total units required by the department requiring the fewer total units. Since Physics requires 360 units, the lowest possible minimum for a Dual Degree with Physics is 450 units.

Minor in Physics

The Minor in Physics is designed to provide a solid foundation in physics at the introductory level, followed by elective courses which will familiarize the student with areas of modern physics, and the concepts and techniques employed therein. The physics minor requires seven courses of at least 9 units each, of which four are required and three are electives.

The Minor is open to all students in the university, but students with non-calculus-based majors should be aware of the mathematics requirements for many physics courses (21-120, 21-122, and 21-259). Students are required to have successfully completed at least one physics course at Carnegie Mellon before declaring the minor, and should declare the minor no later than the add date of their final semester. Interested students should contact Dr. Gillian Ryan, Director of Undergraduate Affairs, and complete the minor declaration form with her assistance.

		Units
33-121	Physics I for Science Students	12
or 33-141	Physics I for Engineering Students
or 33-151	Matter and Interactions I
Corequisite for 33-121 or 33-141 is 21-120 & for 33-151 is 21-122
33-122	Physics II for Biological Sciences & Chemistry Students	12
or 33-142	Physics II for Engineering and Physics Students
or 33-152	Matter and Interactions II
Corequisite for 33-122 or 33-142 is 21-122 & for 33-152 is 21-259
33-104	Experimental Physics	9
33-211	Physics III: Modern Essentials	10
33-xxx	Three Qualifying Physics Electives or Physics Core Electives ²⁵	27-36
Total Physics Minor Units		70-79

_{[25] The physics electives are decided after consultation with, and approval by, the Director of Undergraduate Affairs. Students may take courses from the Qualifying Physics List or additional courses from the Physics Core list, such as Quantum Physics or Electronics I.}

Transfer Credit Requests

Requests for transfer credit for undergraduate physics classes should be made through the student’s home college to the Director of Undergraduate Affairs. Students should contact their departmental academic advisor for the transfer request process in their college. Requests should not be made from students directly to the Department of Physics. It is recommended that requests be placed before paying tuition for a class in case transfer credit is denied. Requests may take 1-2 weeks to be processed by the Department of Physics.

Criteria for Transfer

In assessing the suitability of courses for transfer credit, the Department of Physics will consider the following factors:

The academic rigor of the course must be comparable to that offered at Carnegie Mellon University. This is usually assessed via the course prerequisites and corequisites, the textbook used, and the amount of time spent on topic areas. Completely online classes without in-person proctored examinations do not meet our standard for transfer credit.
The mathematical rigor of a course must also be comparable to that for the CMU course for which a transfer is requested. For example, a class that has no math prerequisite is unlikely to transfer as a CMU class for which there is such a prerequisite, and algebra-based Physics I or Physics II classes will not be accepted for transfer as our calculus-based courses.
The topic areas of a given class and time devoted to each topic should match to a degree of at least 80% those covered in the comparable physics course at Carnegie Mellon University, although this criterion alone is not sufficient to merit transfer. Classes that meet this criterion may still be denied transfer credit if key topics are found to be excluded or if the above mentioned requirements regarding rigor are not met.

Requirements for Transfer Requests

The Department of Physics requires all the following materials to determine if transfer is recommended:

Name of course and its home institution
Number of credits/units/contact hours per week
Course syllabus
Official catalog course description and list of topics covered in the course
A list of all prerequisite and corequisite courses, and official catalog course descriptions of these courses
Required textbook (name, author, and link to information about the text required)

Transfer requests that do not include all information above will not be recommended.

Course Descriptions

About Course Numbers:

Each Carnegie Mellon course number begins with a two-digit prefix that designates the department offering the course (i.e., 76-xxx courses are offered by the Department of English). Although each department maintains its own course numbering practices, typically, the first digit after the prefix indicates the class level: xx-1xx courses are freshmen-level, xx-2xx courses are sophomore level, etc. Depending on the department, xx-6xx courses may be either undergraduate senior-level or graduate-level, and xx-7xx courses and higher are graduate-level. Consult the Schedule of Classes each semester for course offerings and for any necessary pre-requisites or co-requisites.

33-100 Basic Experimental Physics: All Semesters: 6 units
This course provides students with a basic introduction to experimental physics. The content of the course and the particular experiments to be carried out are chosen to be especially useful for students who intend to work in the health sciences. Specific topics will range from mechanics to nuclear and atomic physics. This course is specifically geared toward pre-health students.

33-101 Physics First Year Seminar: Fall and Spring
Various seminars are offered that introduce first-year students to current topics of modern physics. These are mini courses that meet for half a semester. In the past, seminar topics have included: Science and Science Fiction, Astrophysics, Black Holes, Cosmology and Supernovae, Elementary Particles, and The Building Blocks of Matter. These seminars are open only to MCS first year students.

33-104 Experimental Physics: All Semesters: 9 units
This course provides first year students and sophomores with an introduction to the methods of experimental physics. Particular emphasis is placed on three aspects of experimentation: laboratory technique, including both the execution and the documentation of an experiment; data analysis, including the treatment of statistical and systematic errors and computer-aided analysis of experimental data; and written communication of experimental procedures and results. The concepts and skills for measurement and data analysis are acquired gradually through a series of experiments covering a range of topics from mechanics to nuclear and atomic physics.

33-114 Physics of Musical Sound: Spring: 9 units
An introduction to the physics and psychophysics of musical sound. Elementary physics of vibrating systems. Propagation of sound: traveling waves, reflection, and diffraction. Addition of waves: interference and beats. Anatomy of the ear and the perception of sound: loudness, pitch, and timbre. Standing waves and natural modes. Qualitative description of general periodic systems by Fourier analysis: the harmonic series and complex musical tones. The acoustics of musical instruments including percussion instruments, such as drums, bars, and struck and plucked strings; and instruments exhibiting self-sustained oscillations, including bowed strings, blown pipes, reeds, brasses, and singing. Intervals and consonance, musical scales, tuning and temperament. Basic room and auditorium acoustics. There are no formal prerequisites, but some previous musical experience will be useful.

33-115 Physics for Future Presidents: Fall: 9 units
Countless topics of social and political importance are intimately related to science in general and physics in particular. Examples include energy production, global warming, radioactivity, terrorism, and space travel. This course aims to provide key bits of knowledge based on which such issues can be discussed in a meaningful way, i.e., on the level of arguments and not just vague beliefs. We will cover an unusually wide range of topics, including energy, heat, gravity, atoms, radioactivity, chain reactions, electricity, magnetism, waves, light, weather, and climate. The course is open for all students at CMU.

33-120 Science and Science Fiction: Fall and Spring: 9 units
We will view and critique the science content in a selection of science fiction films, spanning more than 100 years of cinematic history, and from sci-fi TV shows from the past 50+ years. Guided by selected readings from current scientific literature, and aided by order-of-magnitude estimates and careful calculations, we will ponder whether the films are showing things which may fall into one of the following categories: Science fiction at the time of production, but currently possible, due to recent breakthroughs. Possible, in principle, but beyond our current technology. Impossible by any science we know. Topics to be covered include the future of the technological society, the physics of Star Trek, the nature of space and time, extraterrestrial intelligence, robotics and artificial intelligence, biotechnology and more.

33-121 Physics I for Science Students: Fall and Spring: 12 units
This calculus-based course combines the basic principles of mechanics with some quantum physics and relativity to explain nature on both a microscopic and macroscopic scale. The course will build models to describe the universe based on a small number of fundamental physics principles. Some simple computer modeling will be done to develop insight into the solving of problems using Newton's laws. Topics covered will include vectors, momentum, force, gravitation, oscillations, energy, quantum physics, center of mass motion, rotation, angular momentum, statistical physics, and the laws of thermodynamics. No computer experience is needed. Examples illustrating basic principles being presented will be taken from physics, chemistry, and biology. This course has a co-requisite of 21-120.

33-122 Physics II for Biological Sciences & Chemistry Students: Fall and Spring: 9 units
This is the second course in the introductory physics sequence for chemistry and biological science majors. The course will consist of eight portions covering (1) electrostatics and dynamics, (2) electrical circuits, (3) magnetism, (4) waves, (5) optics, (6) diffusive motion, and (7) hydrostatic forces and flow. Emphasis will be put on the application of the underlying physical principles in the study of biology and chemistry. This course has a co-requisite of 21-122.
Prerequisites: (33-121 and 21-120) or (33-151 and 21-120) or (33-141 and 21-120) or (33-111 and 21-120) or (33-131 and 21-120) or (33-106 and 21-120)

33-124 Introduction to Astronomy: Fall: 9 units
Astronomy continues to enjoy a golden age of exploration and discovery. This course presents a broad view of astronomy, straightforwardly descriptive and without any complex mathematics. The goal of the course is to encourage non-technical students to become scientifically literate and to appreciate new developments in the world of science, especially in the rapidly developing field of astronomy. Subjects covered include the solar system, stars, galaxies and the universe as a whole. The student should develop an appreciation of the ever-changing universe and our place within it. Computer laboratory exercises will be used to gain practical experience in astronomical techniques. In addition, small telescopes will be used to study the sky. This course is specifically geared toward non-science/engineering majors.

33-141 Physics I for Engineering Students: Fall and Spring: 12 units
This is a first semester, calculus-based introductory physics course. Basic principles of mechanics and thermodynamics are developed. Topics include vectors, displacement, velocity, acceleration, force, equilibrium, mass, Newton's laws, gravitation, work, energy, momentum, impulse, torque and angular momentum, temperature, heat, equations of state, thermodynamic processes, heat engines, refrigerators, first and second laws of thermodynamics, and the kinetic theory of gases. This course has a co-requisite of 21-120.

33-142 Physics II for Engineering and Physics Students: Fall and Spring: 12 units
This is the second half of a two-semester calculus-based introductory physics sequence for engineering and physics students. Two fifths of the course covers electricity, including electrostatics and electric fields, Gauss' law, electric potential, and simple circuits. Two fifths cover magnetism, including magnetic forces, magnetic fields, induction and electromagnetic radiation. One fifth of the course covers mechanical waves (including standing and traveling waves, superposition, and beats) and electromagnetic waves (including mode of propagation, speed, and other properties). This course has a co-requisite of 21-122.
Prerequisites: (33-106 and 21-120) or (33-141 and 21-120) or (21-120 and 33-111) or (33-131 and 21-120) or (33-151 and 21-120) or (21-120 and 33-121)

33-151 Matter and Interactions I: Fall: 12 units
For students with a strong physics background who are interested in using calculus-based mechanics to learn about topics such as dark matter, particle physics, and quantum phenomena, Matter and Interactions I provides an excellent alternative to Physics for Science Students. This course places great emphasis on constructing and using physical models, with a special focus on computer modeling to solve problems. Throughout the course, both traditional analytics techniques and scientific computing will be used to solve mechanical problems going from planetary systems, spring-based systems and nuclear scattering. Topics covered include Newton's Laws, microscopic models of solids, energy, energy quantization, mass-energy equivalence, multi particle systems, collisions, angular momentum including quantized angular momentum, kinetic theory of gases and statistical mechanics. Students conduct team research projects that will be presented at a departmental poster session at the end of the semester. This course has a co-requisite of 21-122.
Prerequisite: 21-120

33-152 Matter and Interactions II: Spring: 12 units
A more challenging alternative to 33-142, Physics II for Engineering and Physics Students. There is an emphasis on atomic-level description and analysis of matter and its electric and magnetic interactions. Topics include: Coulomb's law, polarization, electric field, plasmas, field of charge distributions, microscopic analysis of resistor and capacitor circuits, potential, macroscopic analysis of circuits, Gauss' law, magnetic field, atomic model of magnetism, Ampere's law, magnetic force, relativistic issues, magnetic induction with emphasis on non-Coulomb electric field, Maxwell's equations, electromagnetic radiation including its production and its effects on matter, re-radiation, interference. There will also be computer modeling, visualization and desktop experiments.
Prerequisites: (33-151 and 21-122) or (21-122 and 33-131)

33-201 Physics Sophomore Colloquium I: Fall: 2 units
This course (together with 33-202) is designed to give students an overview of the field of Physics and to help students make knowledgeable choices in both their academic and professional careers. We discuss several of the subfields of Physics in order to give students an understanding of the types of activities, from research to industrial applications, in each. Over the two semesters, we typically discuss six subfields in some detail with the goal of providing a minimal literacy in the relevant concepts and language. The course consists of one classroom lecture per week plus one hour per week of reading and/or problem solving.

33-202 Physics Sophomore Colloquium II: Spring: 2 units
This course is the second in a sequence (following 33-201) designed to give students an overview of the field of Physics and to help students make knowledgeable choices in both their academic and professional careers. We discuss several of the sub-fields of Physics in order to give students an understanding of the types of activities, from research to industrial applications, in each. Over the two semesters, we typically discuss six subfields in some detail with the goal of providing a minimal literacy in the relevant concepts and language. The course consists of one classroom lecture per week plus one hour per week of reading and/or problem solving.

33-211 Physics III: Modern Essentials: Fall and Spring: 10 units
Physics III is primarily for third-semester students of physics, including all physics majors, but is open to any qualified student who wants an introduction to the physics of the 20th century. The course will have a strong component of Special Relativity, dealing with kinematics and dynamics, but not electricity and magnetism. (See 33-213 description.) It will introduce students to a conceptual theory, which is mathematically simple but (initially) non-intuitive. The course also provides a broad exposure to quantum phenomena and early quantum theory without getting overly mathematical. It leads into the more formal Quantum Physics course (33-234).
Prerequisites: 33-112 or 33-152 or 33-132 or 33-142 or 33-107 or 33-122

33-213 Mini-Course in Special Relativity: Fall and Spring: 4 units
This course spans the first six weeks of 33-211, Physics III: Modern Essentials and should not be taking by students intending to major in physics. It treats the mechanics aspects of special relativity, including topics such as simultaneity, the Lorentz transformation, time dilation, length contraction, space-time geometry, resolving some famous puzzles, and the momentum, mass, and energy relations. The Electricity and Magnetism portions of the subject are deferred until the junior/senior courses in E and amp;M (33-338/33-339). Students may not take this class if they have successfully completed 33-211.
Prerequisites: 33-152 or 33-122 or 33-107 or 33-132 or 33-142 or 33-112

33-224 Stars, Galaxies and the Universe: Fall: 9 units
The study of astronomy has blossomed over the past few decades as a result of new ground-based and space-based telescopes, and with the advantage of fast computers for analysis of the huge quantities of data. As our astronomical horizon expands, we are still able to use the laws of physics to make sense of it all. This course is for students who want to understand the basic concepts in astronomy and what drives astronomical objects and the universe. The course emphasizes the application of a few physical principles to a variety of astronomical settings, from stars to galaxies to the structure and evolution of the universe. Introductory classical physics is required, but modern physics will be introduced as needed in the course. The course is intended for science and engineering majors as well as students in other disciplines with good technical backgrounds. Computer lab exercises will be used to gain practical experience in astronomical techniques. In addition, small telescopes are available for personal sign-out for those who would like to use them, and outdoor observing sessions will be organized as weather permits.
Prerequisites: 33-131 or 33-111 or 33-141 or 33-151 or 33-106 or 33-121

33-225 Quantum Physics and Structure of Matter: Fall: 9 units
This course introduces the basic theory used to describe the microscopic world of electrons, atoms, and photons. The duality between wave-like and particle-like phenomena is introduced along with the deBroglie relations which link them. We develop a wave description appropriate for quanta which are partially localized and discuss the interpretation of these wavefunctions. The wave equation of quantum mechanics is developed and applied to the hydrogen atom from which we extrapolate the structure of the Periodic Table. Other materials-related applications are developed, for example, Boltzmann and quantum statistics and properties of electrons in crystals. This course is intended primarily for non-physics majors who have not taken 33-211.
Prerequisites: 33-142 or 33-152 or 33-107 or 33-122 or 33-112 or 33-132

33-226 Physics of Energy: Spring: 9 units
This course will apply basic science, in particular introductory physics concepts, to a wide variety of topics related to energy. The course will closely follow a widely praised textbook The Physics of Energy, so be divided into 3 parts: basic energy science; energy sources; and climate. This course fills the breadth requirement for Physics Majors or can be used as one of the 4 electives required for the Applied Physics Track.
Prerequisites: 33-152 or 33-122 or 33-142

33-228 Electronics I: Spring: 10 units
An introductory laboratory and lecture course with emphasis on elementary circuit analysis, design, and testing. We start by introducing basic circuit elements and study the responses of combinations to DC and AC excitations. We then take up transistors and learn about biasing and the behavior of amplifier circuits. The many uses of operational amplifiers are examined and analyzed; general features of feedback systems are introduced in this context. Complex functions are used to analyze all of the above linear systems. Finally, we examine and build some simple digital integrated circuits.
Prerequisites: 33-112 or 33-132 or 33-107 or 33-142 or 33-152 or 33-122

33-231 Physical Analysis: Fall: 10 units
This course aims to develop analytical skills and mathematical modeling skills across a broad spectrum of physical phenomena, stressing analogies in behavior of a wide variety of systems. Specific topics include dimensional analysis and scaling in physical phenomena, exponential growth and decay, the harmonic oscillator with damping and driving forces, linear approximations of nonlinear systems, coupled oscillators, and wave motion. Necessary mathematical techniques, including differential equations, complex exponential functions, matrix algebra, and Taylor series, are introduced as needed.
Prerequisites: 21-122 and (33-142 or 33-122 or 33-152)

33-232 Mathematical Methods of Physics: Spring: 10 units
This course introduces, in the context of physical systems, a variety of mathematical tools and techniques that will be needed for later courses in the physics curriculum. Topics will include linear algebra, Fourier series and transforms, vector calculus with physical applications, and a first look at partial differential equations. The techniques taught here are useful in more advanced courses such as Physical Mechanics, Electricity and Magnetism, and Advanced Quantum Physics.
Prerequisite: 33-231

33-234 Quantum Physics: Spring: 10 units
An introduction to the fundamental principles and applications of quantum physics. A brief review of the experimental basis for quantization motivates the development of the Schrodinger wave equation. Several unbound and bound problems are treated in one dimension. The properties of angular momentum are developed and applied to central potentials in three dimensions. The one electron atom is then treated. Matrix description of quantum physics and the notion of spin are introduced. Properties of collections of indistinguishable particles are developed allowing an understanding of the structure of the Periodic Table of elements. A variety of mathematical tools are considered as needed.
Prerequisite: 33-211

33-241 Introduction to Computational Physics: Fall: 9 units
This undergraduate course will provide an introduction to the numerical methods and computational algorithms used to solve a variety of problems in physics. In introductory physics courses, you are able to derive analytical solutions for simpler problems and often with simplifying assumptions. Have you wondered if a numerical solution can be obtained for a more complex problem that has no closed-form analytical solution? Computational physics provides a modern and powerful approach to compliment classical approaches to problem solving. Today's and tomorrow's scientists must be computationally fluent to be competitive and successful. In this course, you will learn to formulate problems by applying physical principles, select and apply numerical methods, develop and apply computational algorithms, solve physical problems analytically and numerically, and visualize quantitative results using plotting software.
Prerequisites: 15-112 and 21-122 and 33-104 and (33-152 or 33-142 or 33-107 or 33-112 or 33-132 or 33-122)

33-301 Physics Upperclass Colloquium I: Fall: 1 unit
Junior and senior Physics majors meet together for 1 hour a week to hear discussions on current physics research from faculty, undergraduate and graduate students, and outside speakers. Other topics of interest such as application to graduate school, areas of industrial research and job opportunities will also be presented.

33-302 Physics Upperclass Colloquium II: Spring: 1 unit
Continuation of 33-301: Junior and senior Physics majors meet together for 1 hour a week to hear discussions on current physics research from faculty, undergraduate and graduate students, and outside speakers. Other topics of interest such as application to graduate school, areas of industrial research and job opportunities will also be presented.

33-331 Physical Mechanics I: Fall: 10 units
Fundamental concepts of classical mechanics. Conservation laws, momentum, energy, angular momentum, Lagrange's and Hamilton's equations, motion under a central force, scattering, cross section, and systems of particles.
Prerequisites: 33-231 and 33-232 and 21-259

33-332 Physical Mechanics II: Spring: 10 units
This is the second semester of a two-semester course on classical mechanics. The course will use the tools developed in 33-331 to examine motion in non-inertial reference frames; in particular, rotating frames. This then leads to the development of general rigid body motion, Euler's Equations. Finally, the course will cover coupled oscillations with particular emphasis on normal modes.
Prerequisite: 33-331

33-338 Intermediate Electricity and Magnetism I: Fall: 10 units
This course includes the basic concepts of electro- and magnetostatics. In electrostatics, topics include the electric field and potential for typical configurations, work and energy considerations, the method of images and solutions of Laplace's Equation, multipole expansions, and electrostatics in the presence of matter. In magnetostatics, the magnetic field and vector potential, magnetostatics in the presence of matter, properties of dia-, para- and ferromagnetic materials are developed.
Prerequisites: 33-231 and 21-259 and 33-232

33-339 Intermediate Electricity and Magnetism II: Spring: 10 units
This course focuses on electro- and magnetodynamics. Topics include Faraday's Law of induction, electromagnetic field momentum and energy, Maxwell's equations and electromagnetic waves including plane waves, waves in non-conducting and conducting media, reflection and refraction of waves, and guided waves. Electromagnetic radiation theory includes generation and characteristics of electric and magnetic dipole radiation. The Special Theory of Relativity is applied to electrodynamics: electric and magnetic fields in different reference frames, Lorentz transformations, four-vectors, invariants, and applications to particle mechanics.
Prerequisite: 33-338

33-340 Modern Physics Laboratory: Spring: 10 units
Emphasis is on hands-on experience observing important physical phenomena in the lab, advancing the student's experimental skills, developing sophisticated data analysis techniques, writing thorough reports, and improving verbal communication through several oral progress reports given during the semester and a comprehensive oral report on one experiment. Students perform three experiments which are drawn from the areas of atomic, condensed matter, classical, and nuclear and particle physics. Those currently available are the following: Zeeman effect, light scattering, optical pumping, thermal lensing, Raman scattering, chaos, magnetic susceptibility, nuclear magnetic resonance, electron spin resonance, X-ray diffraction, M and #246;ssbauer effect, neutron activation of radioactive nuclides, Compton scattering, and cosmic ray muons.
Prerequisites: 33-234 and (33-338 or 33-341 or 33-331)

33-341 Thermal Physics I: Fall: 10 units
The three laws of classical thermodynamics, which deal with the existence of state functions for energy and entropy and the entropy at the absolute zero of temperature, are developed along phenomenological lines. Elementary statistical mechanics is then introduced via the canonical ensemble to understand the interpretation of entropy in terms of probability and to calculate some thermodynamic quantities from simple models. These laws are applied to deduce relationships among heat capacities and other measureable quantities and then are generalized to open systems and their various auxiliary thermodynamic potentials; transformations between potentials are developed. Criteria for equilibrium of multicomponent systems are developed and applied to phase transformations and chemical reactions. Models of solutions are obtained by using statistical mechanics and are applied to deduce simple phase diagrams for ideal and regular solutions. The concept of thermodynamic stability is then introduced and illustrated in the context of phase transformations.
Prerequisites: 33-232 and 33-234 and 33-231

33-342 Thermal Physics II: Spring: 10 units
This course begins with a more systematic development of formal probability theory, with emphasis on generating functions, probability density functions and asymptotic approximations. Examples are taken from games of chance, geometric probabilities and radioactive decay. The connections between the ensembles of statistical mechanics (microcanonical, canonical and grand canonical) with the various thermodynamic potentials is developed for single component and multicomponent systems. Fermi-Dirac and Bose-Einstein statistics are reviewed. These principles are then applied to applications such as electronic specific heats, Einstein condensation, chemical reactions, phase transformations, mean field theories, binary phase diagrams, paramagnetism, ferromagnetism, defects, semiconductors and fluctuation phenomena.
Prerequisite: 33-341

33-350 Undergraduate Research: Fall and Spring
Open to sophomore, junior, and senior physics majors. The student undertakes a project of interest under the supervision of a faculty member for 3 to 9 units of credit. May include research done in a research lab, extending the capabilities of a teaching lab, or a theoretical or computational physics project. The student experiences the less structured atmosphere of a research program where there is much room for independent initiative. Student should contact faculty directly to inquire about opportunities. Registration requires approval of the Director of Undergraduate Affairs.

33-353 Intermediate Optics: Fall: 12 units
Offered alternative years. Geometrical optics: reflection and refraction, mirrors, prisms, lenses, apertures and stops, simple optical instruments, fiber optics. Scalar wave optics: wave properties of light, interference, coherence, interferometry, Huygens-Fresnel principle, Fraunhofer diffraction, resolution of optical instruments, Fourier optics, Fresnel diffraction. Laser beam optics: Gaussian beams. Vector wave optics: electromagnetic waves at dielectric interfaces, polarized light. The course will use complex exponential representations of electromagnetic waves.
Prerequisites: 33-122 or 33-142 or 33-112 or 33-132 or 33-107 or 33-152

33-355 Nanoscience and Nanotechnology: Fall: 9 units
This course will explore the underlying science behind nanotechnology, the tools used to create and characterize nanostructures, and potential applications of such devices. Material will be presented on a level intended for upper-level science and engineering students. The course will start with a survey of physics at different length scales, and introduce the application of elementary quantum mechanics and solid-state physics to nanoscience and nanotechnology. Characterization using electron microscopy, scanning probe methods, and spectroscopic techniques will then be described in detail. Fabrication using top-down and bottom-up methods will be discussed, contrasting these approaches and providing examples of each. Nanotechnology methods will be compared with those used in the modern microelectronics industry. Finally, examples of nanoscale components and systems will be described, which may include semiconductor heterostructures; nanotubes and graphene; single-electron transistors; nanoscale magnetic devices; photonic devices; nanofluidic devices; nano electrical-mechanical systems (NEMS); and superconducting devices. There will be time allocated to other topics, with the mutual agreement of the instructor and the class. Stand-alone laboratory exercises will be included as an important element of the course. These will focus on the use of scanning probe methods to study the nm-scale structure and atomic forces involved in various nanostructures as well as micro-scale patterning using photolithography. In addition to the prerequisites, students should have taken a prior laboratory course in a science or engineering department and should have some familiarity with differential equations at an elementary level.
Prerequisites: 33-234 or 33-225

33-398 Special Topics: Fall: 9 units
The description of most all physical systems relies on the concept of a manifold. In addition to the space-time manifold, which plays the role of the stage upon which the dynamics plays out, many systems involve target spaces which are manifolds. These target spaces are typically Lie Groups. A classic example of such a system is the rigid rotator, where every configuration of the system is a point on the manifold which defines the group of rotations. The purpose of this class will be to learn the basics of differential geometry and apply these ideas to physical systems. Topics will include Hamiltonian dynamics, fluid mechanics as well as gauge theories. Requirements: Knowledge of Linear Algebra. No prior knowledge of group theory will be expected.
Prerequisites: (21-260 or 33-231) and 21-341

33-441 Introduction to Biophysics: Fall: 10 units
Biological physics, or the physics of living systems, is an exciting interdisciplinary frontier of physics that aims to understand the phenomenon of life using concepts and tools from Physics. This intermediate level course will introduce the general concepts and principles underpinning the physical behavior of living systems, from the dynamics of proteins and molecules to collective behavior of living cells and organisms. The course will develop key physics concepts that are most vital to biological processes, including energy conversion, information transfer, mechanics of movement, statistical phenomena, and fluid flow. We will apply these physics concepts to demonstrate how biological systems function, build simplified mathematical models to predict behavior, and use experimental data to inform and test models. The integration of biological phenomena, physical concepts, mathematical modeling, and analysis of experimental data represents an entirely new mode of learning, based on strategies adopted in research. These strategies will break traditional disciplinary barriers between physics and biology. The students will be expected to gain an intuitive grasp of ways to: frame the physical problem, identify appropriate theoretical frameworks, analyze experimental data, and ways to generalize and to understand the dependence of biophysical phenomenon on time and length scales. No prior knowledge of biology is expected. This class is offered in Fall of even years (e.g. Fall '24, 26, etc.)
Prerequisites: 33-142 or 33-112 or 33-152 or 33-107 or 33-132 or 33-122

33-444 Introduction to Nuclear and Particle Physics: Spring: 9 units
Description of our understanding of nuclei, elementary particles, and quarks, with equal emphasis on the nuclear and particle aspects of sub-atomic matter. We discuss the physics of accelerators, and how particle interactions with matter lead to various kinds of detector instrumentation. Then we discuss methods for measuring sub-atomic structure, symmetries and conservation laws, and the electromagnetic, weak, and strong interactions. We examine the quark model of the mesons and baryons, as well as several models of the atomic nucleus. This class is offered in Spring of even years (e.g. Spring '24, '26, etc.)
Prerequisites: 33-234 and 33-338

33-445 Advanced Quantum Physics I: Fall: 9 units
Mathematics of quantum theory, linear algebra and Hilbert spaces; review of classical mechanics; problems with classical mechanics; postulates of quantum theory; one dimensional applications; the harmonic oscillator; uncertainty relations; systems with N degrees of freedom, multi-particle states, identical particles; approximation methods. This course has a co-requisite of 33-331.
Prerequisite: 33-234

33-446 Advanced Quantum Physics II: Spring: 9 units
Classical symmetries; quantum symmetries; rotations and angular momentum; spin; addition of angular momentum; the hydrogen atom; quantum "paradoxes" and Bell's theorem; applications.
Prerequisite: 33-445

33-448 Introduction to Solid State Physics: Spring: 9 units
This course gives a quantitative description of crystal lattices, common crystal structures obtained by adding a basis of atoms to the lattice, and the definition and properties of the reciprocal lattice. Diffraction measurements are studied as tools to quantify crystal lattices, including Bragg's law and structure factors. Diffraction from amorphous substances and liquids is also introduced. The various types of atomic bonding, e.g., Van der Waals, metallic, ionic, covalent and hydrogen are surveyed. Binding energies of some crystalline structures are calculated. Models of crystal binding are generalized to include dynamics, first for classical lattice vibrations and then for quantized lattice vibrations known as phonons. These concepts are used to calculate the heat capacities of insulating crystals, to introduce the concept of density of states, and to discuss phonon scattering. The band theory of solids is developed, starting with the free electron model of a metal and culminating with the properties of conductors and semiconductors. Magnetic phenomena such as paramagnetism and the mean field theory of ferromagnetism are covered to the extent that time permits.
Prerequisites: 33-341 and (33-225 or 33-234)

33-451 Senior Research: Fall and Spring
Open to all senior physics majors. May include research done in a research lab, extending the capabilities of a teaching lab, or a theoretical or computational physics project for 3 to 9 units of credit. The student experiences the less structured atmosphere of a research program where there is much room for independent initiative. Modern Physics Laboratory, 33-340, should precede this course, though it is not required. Student should contact faculty directly to inquire about opportunities. Registration requires approval of the Director of Undergraduate Affairs.

33-456 Advanced Computational Physics: Spring: 9 units
This course uses techniques covered in Introduction to Computational Physics as a foundation. Major topics in the course will be Data Science, Parallel Computing and Machine Learning with applications from astrophysics, thermodynamics, orbital mechanics and other domains. The course will introduce professional practices such as compiling and optimizing code, using software development environments and software engineering. Students will gain a practical knowledge of current computing hardware design, the C computer language, the TensorFlow deep learning framework and the Spark big data platform, while using a Linux supercomputing environment.
Prerequisite: 33-241

33-466 Extragalactic Astrophysics and Cosmology: Spring: 9 units
Starting from the expanding universe of galaxies, this course lays out the structure of the universe from the Local Group of galaxies to the largest structures observed. The observational pinnacle of the Big Bang theory, the microwave background radiation, is shown to provide us with many clues to conditions in the early universe and to the parameters which control the expansion and fate of the universe. Current theories for the development of galaxies and clusters of galaxies are outlined in terms of our current understanding of dark matter. Observational cosmology continues to enjoy a golden era of discovery and the latest observational results will be interpreted in terms of the basic cosmological parameters.
Prerequisites: 33-224 and 33-234

33-467 Astrophysics of Stars and the Galaxy: Fall: 9 units
The physics of stars is introduced from first principles, leading from star formation to nuclear fusion to late stellar evolution and the end points of stars: white dwarfs, neutron stars and black holes. The theory of stellar structure and evolution is elegant and impressively powerful, bringing together all branches of physics to predict the life cycles of the stars. The basic physical processes in the interstellar medium will also be described, and the role of multi-wavelength astronomy will be used to illustrate our understanding of the structure of the Milky Way Galaxy, from the massive black hole at the center to the halo of dark matter which emcompasses it. This class is offered in Fall of odd years (e.g. Fall '23, 25, etc.)
Prerequisites: 33-224 and 33-234

33-499 Supervised Reading: Fall and Spring
Physics majors may explore a certain area of advanced physics under the direct supervision of a faculty member for up to 9 units of credit. Special permission is required from the Director for Undergraduate Affairs to register. The student must contact a faculty member directly to inquire about opportunities, and to develop a written plan that includes a list of topics to be covered, expectations of student time and/or work, as well as a description of how student learning will be evaluated. The Director of Undergraduate Affairs will review this plan and students will be registered only if the plan is approved.

Please note the following corequisites:

33-121: Corequisite is 21-120
33-122: Corequisite of 21-122
33-151: Corequisite is 21-122
33-152: Corequisite is 21-259
33-141: Corequisite is 21-120
33-142: Corequisite is 21-122

Faculty

JOHN ALISON, Associate Professor of Physics – Ph.D., University of Pennsylvania; Carnegie Mellon, 2018–

DAVID ANDERSON, Associate Teaching Professor of Physics – Ph.D., University of York (UK) ; Carnegie Mellon, 2008–

SHILADITYA BANERJEE, Associate Professor of Physics – Ph.D., Syracuse University; Carnegie Mellon, 2020–

KATELYN BREIVIK, Assistant Professor of Physics – Ph.D., Northwestern University; Carnegie Mellon, 2023–

ROY A. BRIERE, Professor of Physics – Ph.D., University of Chicago; Carnegie Mellon, 1999–

SHUBHAYU CHATTERJEE, Assistant Professor of Physics – Ph.D., Harvard University; Carnegie Mellon, 2023–

HAEL COLLINS, Assistant Teaching Professor of Physics – Ph.D., Harvard University; Carnegie Mellon, 2019–

MATTEO CREMONESI, Assistant Professor of Physics – Ph.D., Oxford University; Carnegie Mellon, 2022–

RUPERT CROFT, Professor of Physics – Ph.D., Oxford University; Carnegie Mellon, 2001–

MARKUS DESERNO, Professor of Physics; Director of Graduate Studies, Department of Physics – Ph.D., University of Mainz, Germany; Carnegie Mellon, 2007–

TIZIANA DI MATTEO, Professor of Physics – Ph.D., University of Cambridge; Carnegie Mellon, 2005–

VALENTINA DUTTA, Assistant Professor of Physics – Ph.D., Massachusetts Institute of Technology; Carnegie Mellon, 2022–

SCOTT DODELSON, Professor of Physics – Ph.D., Columbia University; Carnegie Mellon, 2017–

RANDALL M. FEENSTRA, Professor of Physics – Ph.D., California Institute of Technology; Carnegie Mellon, 1995–

FRANK HEINRICH, Associate Research Professor of Physics – Ph.D., University of Leipzig; Carnegie Mellon, 2008–

BENJAMIN HUNT, Associate Professor of Physics – Ph.D., Cornell University; Carnegie Mellon, 2015–

TINA KAHNIASHVILI, Research Professor of Physics – Ph.D., Russian Academy of Sciences; Carnegie Mellon, 2010–

JYOTI KATOCH, Associate Professor or Physics – Ph.D., University of Central Florida; Carnegie Mellon, 2018–

VLADYSLAV KOZII, Assistant Professor of Physics – Ph.D., Massachusetts Institute of Technology; Carnegie Mellon, 2022–

BARRY B. LUOKKALA, Teaching Professor of Physics – Ph.D., Carnegie Mellon University; Carnegie Mellon, 1988–

SARA A. MAJETICH, Professor of Physics – Ph.D., University of Georgia; Carnegie Mellon, 1990–

RACHEL MANDELBAUM, Professor of Physics; Interim Department Head, Department of Physics – Ph.D., Princeton University; Carnegie Mellon, 2011–

CURTIS A. MEYER, Professor of Physics; Associate Dean, Mellon College of Science – Ph.D., University of California, Berkeley; Carnegie Mellon, 1993–

COLIN J. MORNINGSTAR, Professor of Physics – Ph.D., University of Toronto; Carnegie Mellon, 2000–

BRENDAN MULLAN, Associate Teaching Professor; Director of Undergraduate Laboratories, Department of Physics – Ph.D., Pennsylvania State University; Carnegie Mellon, 2024–

ANTONELLA PALMESE, Assistant Professor of Physics – Ph.D., University College London; Carnegie Mellon, 2022–

DIANA S. PARNO, Associate Professor of Physics – Ph.D., Carnegie Mellon University; Carnegie Mellon, 2017–

MANFRED PAULINI, Professor of Physics; Associate Dean, Mellon College of Science – Ph.D., University of Erlangen, Germany; Carnegie Mellon, 2000–

RICCARDO PENCO, Associate Professor of Physics – Ph.D., Syracuse University; Carnegie Mellon, 2018–

JEFFREY B. PETERSON, Professor of Physics – Ph.D., University of California, Berkeley; Carnegie Mellon, 1993–

RACHEL ROSEN, Associate Professor of Physics – Ph.D., New York University; Carnegie Mellon, 2023–

IRA Z. ROTHSTEIN, Professor of Physics – Ph.D., University of Maryland at College Park; Carnegie Mellon, 1997–

GILLIAN LYNN RYAN, Associate Teaching Professor of Physics; Director of Undergraduate Affairs, Department of Physics – Ph.D., Dalhousie University; Carnegie Mellon, 2020–

SUFEI SHI, Associate Professor of Physics – Ph.D., Cornell University; Carnegie Mellon, 2023–

FANGWEI SI, Assistant Professor of Physics – Ph.D., Johns Hopkins University; Carnegie Mellon, 2022–

SIMRANJEET SINGH, Assistant Professor of Physics – Ph.D., University of Central Florida; Carnegie Mellon, 2018–

GRIGORY TARNOPOLSKY, Assistant Professor of Physics – Ph.D., Princeton University; Carnegie Mellon, 2021–

HY TRAC, Associate Professor of Physics – Ph.D., University of Toronto; Carnegie Mellon, 2010–

MATTHEW WALKER, Associate Professor of Physics – Ph.D., University of Michigan; Carnegie Mellon, 2013–

MICHAEL WIDOM, Professor of Physics – Ph.D., University of Chicago; Carnegie Mellon, 1985–

Emeriti Faculty

LUC BERGER, Professor of Physics, Emeritus – Ph.D., University of Lausanne, Switzerland; Carnegie Mellon, 1960–

ARNOLD ENGLER, Professor of Physics, Emeritus – Ph.D., University of Berne, Switzerland; Carnegie Mellon, 1962–

THOMAS A. FERGUSON, Professor of Physics, Emeritus – Ph.D., University of California at Los Angeles; Carnegie Mellon; Carnegie Mellon, 1985–

JOHN G. FETKOVICH, Professor of Physics, Emeritus – Ph.D., Carnegie Mellon University; Carnegie Mellon, 1959–

GREGG B. FRANKLIN, Professor of Physics – Ph.D., Massachusetts Institute of Technology; Carnegie Mellon, 1984–

STEPHEN GAROFF, Professor of Physics – Ph.D., Harvard ; Carnegie Mellon, 1988–

FREDERICK J. GILMAN, Professor of Physics, Emeritus – Ph.D., Princeton University; Carnegie Mellon, 1995–

RICHARD GRIFFITHS, Professor of Physics, Emeritus – Ph.D., University of Leicester, U.K.; Carnegie Mellon, 1996–

ROBERT GRIFFITHS, University Professor of Physics, Emeritus – Ph.D, Stanford University; Carnegie Mellon, 1962–

LEONARD S. KISSLINGER, Professor of Physics, Emeritus – Ph.D., Indiana University; Carnegie Mellon, 1969–

GEORGE KLEIN, Associate Teaching Professor of Physics – Ph.D., New York University; Carnegie Mellon, 1993–

ROBERT W. KRAEMER, Professor of Physics, Emeritus – Ph.D., Johns Hopkins University; Carnegie Mellon, 1965–

MICHAEL J. LEVINE, Professor of Physics, Emeritus – Ph.D., California Institute of Technology; Carnegie Mellon, 1968–

LING-FONG LI, Professor of Physics, Emeritus – Ph.D., University of Pennsylvania; Carnegie Mellon, 1974–

MATHIAS LOSCHE, Professor of Physics – Ph.D., Technical University of Munich; Carnegie Mellon, 2005–

JOHN F. NAGLE, Professor of Physics, Emeritus – Ph.D., Yale University; Carnegie Mellon, 1967–

BRIAN P. QUINN, Professor of Physics, Emeritus – Ph.D., Massachusetts Institute of Technology; Carnegie Mellon, 1988–

JAMES S. RUSS, Professor of Physics, Emeritus – Ph.D., Princeton University; Carnegie Mellon, 1967–

REINHARD SCHUMACHER, Professor of Physics, Emeritus – Ph.D., Massachusetts Institute of Technology; Carnegie Mellon, 1987–

ROBERT F. SEKERKA, University Professor of Physics and Mathematics, Emeritus – Ph.D., Harvard ; Carnegie Mellon, 1969–

ROBERT M. SUTER, Professor of Physics, Emeritus – Ph.D., Clark University; Carnegie Mellon, 1981–

ROBERT H. SWENDSEN, Professor of Physics, Emeritus – Ph.D., University of Pennsylvania; Carnegie Mellon, 1984–

STEPHANIE TRISTRAM-NAGLE, Research Professor of Physics, Emerita – Ph.D., University of California, Berkeley; Carnegie Mellon, 1986–

NED S. VANDER VEN, Professor of Physics, Emeritus – Ph.D., Princeton University; Carnegie Mellon, 1961–

HELMUT VOGEL, Professor of Physics, Emeritus – Ph.D. , University of Erlangen-Nuremberg; Carnegie Mellon, 1983–

Joint Appointments and Courtesy Appointments

SHELLEY ANNA, Professor of Chemical Engineering – Ph.D., Harvard University; Carnegie Mellon, 2003–

AXEL BRANDENBURG, Adjunct Professor of Physics – Ph.D., University of Helsinki; Carnegie Mellon, 2018–

SHIRLEY HO, Adjunct Associate Professor of Physics – Ph.D., Princeton University; Carnegie Mellon, 2012–

MOHAMMAD F. ISLAM, Associate Research Professor of Materials Science & Engineering – Ph.D., University of Pennsylvania; Carnegie Mellon, 2005–

NOA MAROM, Assistant Professor of Material Science and Engineering – Ph.D., Weizmann of Science; Carnegie Mellon, 2016–

MICHAEL E. MCHENRY, Professor of Materials Science and Engineering – Ph.D., Massachusetts Institute of Technology; Carnegie Mellon, 1989–

CARL RODRIGUEZ, Adjunct Professor of Physics – Ph.D., Northwestern University; Carnegie Mellon, 2023–

ANTHONY D. ROLLETT, Professor of Materials Science & Engineering – Ph.D., Drexel University; Carnegie Mellon, 1995–

MAREK SKOWRONSKI, Professor of Material Science and Engineering – Ph.D., Warsaw University; Carnegie Mellon, 1988–

VENKAT VISWANATHAN, Assistant Professor of Mechanical Engineering – Ph.D., Stanford University; Carnegie Mellon, 2014–

HUAIYING ZHANG, Assistant Professor of Biological Sciences – Ph.D., McGill University; Carnegie Mellon, 2022–

JIAN-GANG ZHU, Professor of Electrical and Computer Engineering – Ph.D., University of California San Diego; Carnegie Mellon, 1997–