Department of Physics

B.S. in Physics - Example Schedule

Freshman Year

Fall Units

33-111 Physics for Science Students I 12

or

33-131 Matter and Interactions I 12

15-111 Programming Fundamentals 5

15-112 Object-Based Programming I 5

21-115 Differential Calculus 5

21-116 Integral Calculus 5

99-101 Computing Skills Workshop 3

76-101 Interpretation and Argument 9

44

Spring

33-112 Physics for Science Students II 12

or

33-132 Matter and Interactions II 12

33-104 Experimental Physics 9

21-117 Integration and Differential Equations 5

21-118 Calculus of Approximation 5

xx-xxx Humanities, Social Sciences, or Fine Arts Course 9

40

Sophomore Year

Fall Units

33-211 Physics III: Modern Essentials 10

33-231 Physical Analysis 9

21-260 Differential Equations 9

33-201 Undergraduate Colloquium I 1

09-105 Introduction to Modern Chemistry 10

xx-xxx H&SS/FA Course 9

48

Spring

33-234 Quantum Physics 10

33-228 Electronics 10

33-202 Undergraduate Colloquium II 1

03-121 Modern Biology 9

21-259 Calculus in Three Dimensions 9

xx-xxx H&SS/FA Course 9

48

Junior Year

Fall Units

33-331 Physical Mechanics I 10

33-341 Thermal Physics I 10

33-345 Mathematical Methods of Physics 9

or

xx-xxx Mathematics Elective

xx-xxx Elective 9

33-301 Undergraduate Colloquium III 1

xx-xxx H&SS/FA Course 9

48

Spring

33-332 Physical Mechanics II 10

33-338 Intermediate Electricity and Magnetism I 10

33-340 Modern Physics Laboratory 10

xx-xxx Elective 9

33-302 Undergraduate Colloquium IV 1

xx-xxx H&SS/FA Course 9

49

Senior Year

Fall Units

33-439 Intermediate Electricity and Magnetism II 10

xx-xxx Elective 9

xx-xxx Elective 9

xx-xxx Elective 8

33-401 Undergraduate Colloquium V 1

xx-xxx H&SS/FA Course 9

46

Spring

xx-xxx Elective 9

xx-xxx Elective 9

xx-xxx Elective 9

33-402 Undergraduate Colloquium VI 1

xx-xxx H&SS/FA Course 9

37

B.A. in Physics

With fewer mathematics and technical elective requirements and more free electives, the B.A. degree offers the enhanced opportunity for students to combine the physics degree with intensive work in other non-technical areas.

The requirements for the B.A. degree are the same as those listed above for the B.S. degree with the following changes:

• No units of mathematics elective are required

• No units of technical electives are required

• Free electives now account for 62 units.

The minimum number of units required for this degree is 360.

With the extra units in free electives, a student may, for example, double major with a department in the College of Humanities and Social Sciences, the College of Fine Arts, or Business Administration.

B.S. in Physics / Applied Physics Track

The B.S. in Physics/Applied Physics Track is designed primarily for the student who wants to prepare for a career path which takes advantage of the diverse and expanding opportunities in industrial and government laboratories for the graduate with a B.S. in Applied Physics. 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. To that end, the student will first meet with the Applied Physics Track Advisor to discuss interests and career goals and to choose computing, laboratory and applications electives which fulfill the requirements of the track.

Because of the flexible nature of the track, the student is required to meet with the Track Advisor EVERY SEMESTER prior to registration, in order to have the program of study for the next semester approved. This will insure that the student's course of study satisfies all requirements for graduation.

The requirements for this track are the same as those listed above for the B.S. degree with the following changes:

Additions to the requirements listed for the B.S. in Physics:

• 33-448 Introduction to Solid State Physics

• One course (at least 9 units) which strengthens the student's ability to use the computer as a tool in the research environment. Possible examples include:

33-241 Introduction to Computational Physics

03-310 Introduction to Computational Biology

18-205 Mathematical Software in Engineering (12 units)

• Two courses (at least 18 units) which broaden the student's laboratory skills. (The existence of pre-requisites for some of the desired laboratory classes may require coordination with the student's other electives in Applied Physics.) Possible examples include:

06-313 Experimental Colloid and Surface Science

09-131 Laboratory I: Introduction to Chemical Analysis

12-356 Fluid Mechanics Laboratory

27-303 Materials Science and Engineering Laboratory I

• Two courses (at least 18 units) which give the student experience in applying basic physics principles to a variety of problems. Possible examples include:

33-453 Intermediate Optics

06-607 Physical Chemistry of Colloids and Surfaces

18-100 Introduction to Electrical and Computer Engineering

24-101 Fundamentals of Mechanical Engineering

24-231 Fluid Mechanics

27-100 Materials in Engineering

• 33-451 Senior Research (at least 9 units) The topic in Senior Research must be in Applied Physics, to be approved by the Track Advisor. (Under special circumstances, research for pay may count toward this requirement, though it cannot be counted toward the units required for graduation.)

• 1 Free Elective Unit

Deletions from the requirements listed for the B.S. in Physics:

• 33-332 Physics Mechanics II is NOT required

• No units of Physics Electives are required

• No units of Mathematics Electives are required

• No units of Technical Electives are required

The minimum number of units required for this degree is 360.

B.S. in Physics / 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.

The requirements for this track are the same as those listed above for the B.S. degree with the following changes:

Additions to the requirements listed for the B.S. in Physics:

• 33-224 Stars, Galaxies and the Universe

• 33-467 Introduction to Astrophysics

• 33-466 Introduction to Cosmology

• 33-650 General Relativity

• At least 9 units of Research in Astrophysics - may be taken as either of the following two courses:

33-350 Undergraduate Research

33-451 Senior Research

Deletions from the requirements listed for the B.S. in Physics:

• No units of Physics Electives are required

• No units of Technical Electives are required

The minimum number of units required for this degree is 360.

B.S. in Physics / 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 so that it can readily be adapted to the requirements of individual students.

The Biological Physics Track incorporates a number of courses which are also requirements for the pre-medical program. Students interested in both the Biological Physics Track and the pre-medical program should consult both with their Physics Department advisor and the Director of the Health Professions Program for help in planning their programs.

The requirements for this track are the same as those listed above for the B.S. degree with the following changes:

Additions to the requirements listed for the B.S. in Physics:

• 03-231 Biochemistry I

• 03-439 Introduction to Biophysics

• 09-117 Organic Chemistry

• Two courses from the following list:

03-124 Modern Biology Laboratory

03-130 Biology of Organisms or 42-500 Physiology

03-332 Biochemistry II

03-438 Physical Biochemistry

03-533 NMR in Biomedical Sciences

03-534 Fluorescence Spectroscopy in Biological Research

• 1 Free Elective Unit

Deletions from the requirements listed for the B.S. in Physics:

• 33-332 Physics Mechanics II

• Only 9 units of Physics Electives required

• No units of Technical Electives required

The minimum number of units required for this degree is 360.

B.S. in Physics / 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 school in physics with an emphasis on chemical physics or chemistry.

The Chemical Physics Track incorporates a number of courses which are also requirements for the pre-medical program. Students interested in both the Chemical Physics Track and the pre-medical program should consult both with their Physics Department advisor and the Director of the Health Professions Program for help in planning their programs.

The requirements for this track are the same as those listed above for the B.S. degree with the following changes:

Additions to the requirements listed for the B.S. in Physics:

• 09-106 Modern Chemistry II

• 09-244 Physical Chemistry I (Quantum)

• 09-245 Physical Chemistry II (Thermodynamics)

• Three courses from the following list (at least 27 units):

09-117 Organic Chemistry I

09-131 Laboratory I: Introduction to Chemical Analysis

09-218 Organic Chemistry II

09-232 Laboratory IV: Molecular Spectroscopy and Dynamics

09-248 Inorganic Chemistry

09-441 Nuclear and Radiochemistry

09-445 Undergraduate Research (9-12 units)

09-509 Physical Chemistry of Macromolecules

09-511 Solid State Materials Chemistry

Deletions from the requirements listed for the B.S. in Physics:

• 33-332 Physics Mechanics II

• No units of Physics Electives are required

• No units of Technical Electives are required

The minimum number of units required for this degree is 360.

B.S. in Physics / 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 which are used in the analysis of physical problems and in subjects ranging from control and real-time programming to software engineering and compiler and operating systems design. The degree provides the student with a rigorous grounding in physics as well as in the foundations and practice of computer use as applied to scientific problems. Work is done on machines ranging from high function workstations through supercomputers.

The degree program includes additional courses from the Mathematics and Computer Science Departments as well as special courses in computational physics from the Physics Department. The program can be adapted to special requirements of individual students.

The requirements for this track are the same as those listed above for the B.S. degree with the following changes:

Additions to the requirements listed for the B.S. in Physics:

• 33-241 Introduction to Computational Physics

• 33-456 Advanced Computational Physics

• 21-127 Concepts of Mathematics

• 21-369 Numerical Methods

• 15-113 Object-Based Programming II

(15-113 is a half-semester mini-course.)

• 15-211 Fundamental Data Structures and Algorithms

• 15-212 Principles of Programming

Deletions from the requirements listed for the B.S. in Physics:

• No units of Physics Electives are required

• No units of Mathematics Electives are required

• Only 9 units of Technical Electives are required

• Only 6 units of Free Electives are required

The minimum number of units required for this degree is 360.

B.S. or B.A. in Physics with a Minor in Secondary Education and Teacher Certification in Secondary Education of Physics

As discussed in the general introduction to the Mellon College of Science, students are encouraged to consider careers in secondary education, since there is a serious need for high school teachers who are well trained in physics. Through the cooperative program between the Mellon College of Science and nearby Chatham College, a student can major in physics, earn a minor in secondary education and also qualify for teacher certification in secondary education of physics in Pennsylvania. In this program a student majors in physics at Carnegie Mellon while taking education and psychology courses at Chatham in preparation for practice teaching at a local high school. The requirements for the minor and Teaching Certificate can be found on page 267.

Students interested in teaching at the secondary level can obtain a degree in one of the physics major tracks while concurrently earning a minor in secondary education and qualifying for teacher certification in secondary education of physics in Pennsylvania. In addition to the requirements for the major, six courses must be taken at Chatham College in education and psychology in preparation for a semester of practice teaching at a local high school. As noted in the general introduction to MCS, the degree, including this minor, is granted by Carnegie Mellon, while the teacher certification in Pennsylvania is obtained through Chatham. The required Chatham courses are as follows:

EDU 302 Perspectives on Education (4 credits = 12 units)

EDU 320 Principles of Secondary Education (4 credits = 12 units)

EDU 321 Teaching Methods for the Secondary and Adult Level

(4 credits = 12 units)

EDU 322 Teaching in a Multicultural Setting (4 credits = 12 units)

EDU 326 Content Reading Instruction (4 credits = 12 units)

PSY 325 Tests and Measurements (3 credits = 9 units)

EDU 423 Secondary Student Teaching (12 credits = 36 units).

Note that 1) EDU 302 and EDU 320 can be used to satisfy part of Category C of the H&SS/FA requirements, while the rest of the Chatham courses must be counted as free electives, 2) a prerequisite for PSY 325 is 85-102, Introduction to Psychology, which satisfies Category B1 of the H&SS/FA requirements, and 3) there is also a statistics requirement for PSY 325, which can be waved for physics majors. Also, a student in this program may cross-register at Chatham for more than one course in a given semester.

A student earning a B.A. in Physics can readily complete this program in four years. For a student earning a B.S. in Physics, careful planning is needed. Note in particular that planning for this program should be done in close consultation with the Head of Undergraduate Advising of the Physics Department. It is important that planning begins early since the first course in education should be taken by the second semester of the sophomore year in order to complete the program in minimal time.

A Second Major or a Second Degree in Physics with the Primary Degree in Another Department

Physics may be taken as a second major or for 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.

For Physics as a Second Major with a B.S. or B.A. alone or with any track, all requirements of the degree and track as a primary major must be fulfilled except:

• No units of Mathematics Elective are required

• No units of Technical Electives are required

• No units of Free Electives are required

• No H&SS/FA courses are required

• The following courses in the MCS core are not required: 03-121, 09-105, 99-101. However, 15-111/112 or 15-125 or 15-127 is required.

In order to receive a second degree in physics with a first degree in another home department, all requirements for the particular physics track must be fulfilled. The non-technical requirements will be waived if the home department has a similar set of required courses. Also, the number of units required is 90 more than the total units required by the department requiring the fewer total units.

The Minor in Physics

The Minor in Physics is designed to provide a solid foundation in physics at the introductory level, followed by elective courses in which the student will become familiar with a sample of the many modern areas of physics, and the concepts and techniques employed therein. The sequence consists of two introductory level courses followed by five electives chosen from the below list. The choice of electives requires prior approval by the Department of Physics, and should be made in close consultation with the Physics Department faculty advisor. The Department intends to be flexible and accommodate the student's specific interests. The minor is open to all students of the university, although students with non-calculus based majors should be aware of the mathematics requirements for many physics courses (21-115, 116, 117, 118, 259, 260).

The Physics minor requires 7 courses of at least 9 units each.

Introductory Courses

Choose one course:

33-106 Physics for Engineering Students I

33-111 Physics for Science Students I

33-131 Matter and Interactions I

Choose one course:

33-107 Physics for Engineering Students II

33-112 Physics for Science Students II

33-132 Matter and Interactions II

• Elective Courses

Choose five courses:

33-104 Experimental Physics (*)

33-114 Physics of Musical Sound

33-211 Physics III: Modern Essentials

33-224 Stars, Galaxies and the Universe

33-225 Quantum Physics and Structure of Matter

33-228 Electronics

33-231 Physical Analysis

33-234 Quantum Physics

33-241 Introduction to Computational Physics

33-331 Physical Mechanics I

33-332 Physical Mechanics II

33-338 Intermediate Electricity and Magnetism I

33-340 Modern Physics Laboratory

33-341 Thermal Physics I

33-342 Thermal Physics II

33-345 Mathematical Methods of Physics

33-350 Undergraduate Research

33-439 Intermediate Electricity and Magnetism II

33-444 Introduction to Nuclear & Particle Physics

33-445 Advanced Quantum Physics I

33-446 Advanced Quantum Physics II

33-448 Introduction to Solid State Physics

33-451 Senior Research

33-453 Intermediate Optics

33-456 Advanced Computational Physics

33-458 Special Problems in Computational Physics

33-466 Introduction to Cosmology

33-467 Introduction to Astrophysics

33-650 General Relativity

33-658 Quantum Computation and Information

or other suitable courses listed under 33-xxx.

(*) required if the student does not complete any other laboratory course in science or engineering.

Faculty

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

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

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

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

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

FREDERICK J. GILMAN, Buhl Professor of Physics, Head, Department of Physics — Ph.D., Princeton University; Carnegie Mellon, 1995—.

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

ROBERT B. GRIFFITHS, University Professor & Otto Stern Professor of Physics — Ph.D., Stanford University; Carnegie Mellon, 1964—.

JAMES B. HANNON, Assistant Professor of Physics - Ph.D., University of Pennsylvania; Carnegie Mellon, 1998—.

RICHARD F. HOLMAN, Professor of Physics — Ph.D., Johns Hopkins University; Carnegie Mellon, 1987—.

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

GEORGE KLEIN, Lecturer — Ph.D., New York University; Carnegie Mellon, 1993—.

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

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

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

BARRY B. LUOKKALA, Senior Lecturer/Laboratory Demonstrator — M.S., University of Pittsburgh; Carnegie Mellon, 1990—.

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

CURTIS A. MEYER, Associate Professor of Physics — Ph.D., University of California, Berkeley; Carnegie Mellon, 1993—.

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

JOHN F. NAGLE, Professor of Physics and Biological Sciences — Ph.D., Yale University; Carnegie Mellon, 1967—.

ROBERT C. NICHOL, Assistant Professor of Physics — Ph.D., University of Edinburgh, Scotland; Carnegie Mellon, 1996—.

MANFRED PAULINI, Associate Professor of Physics — Ph.D., University of Erlangen, Germany; Carnegie Mellon, 2000—.

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

BRIAN P. QUINN, Associate Professor of Physics — Ph.D., Massachusetts Institute of Technology; Carnegie Mellon, l988—.

KAVAN U. RATNATUNGA, Senior Research Scientist — Ph.D., Australian National University; Carnegie Mellon, 1996—.

FREDERICK REIF, Professor, Center for Innovation in Learning, Professor of Physics and Psychology — Ph.D., Harvard; Carnegie Mellon, 1990—.

A. KATHERINE ROMER, Assistant Professor of Physics — Ph.D., University of Edinburgh, Scotland; Carnegie Mellon, 1997—.

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

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

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

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

BRUCE A. SHERWOOD, Principal Research Scientist, Center for Innovation in Learning & Professor of Physics — Ph.D., University of Chicago; Carnegie Mellon, 1984—.

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

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

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

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

HUGH D. YOUNG, Professor of Physics — Ph.D., Carnegie Mellon University; Carnegie Mellon, 1956—.

Emeritus Faculty

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

RICHARD M. EDELSTEIN, Professor Emeritus of Physics — Ph.D., Columbia University; Carnegie Mellon, 1960—.

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

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

SIMEON A. FRIEDBERG, Professor Emeritus of Physics — D.Sc., Carnegie Institute of Technology; Carnegie Mellon, 1953—.

JOHN A. RAYNE, Professor Emeritus of Physics — Ph.D., University of Chicago; Carnegie Mellon, 1963—.

ROBERT T. SCHUMACHER, Professor Emeritus of Physics — Ph.D., University of Illinois; Carnegie Mellon, 1957—.

RAYMOND A. SORENSEN, Professor Emeritus of Physics — Ph.D., Carnegie Mellon University; Carnegie Mellon, 1961—.

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

LINCOLN WOLFENSTEIN, University Professor Emeritus of Physics — Ph.D., University of Chicago; Carnegie Mellon, 1948—.

Joint Appointments and Special Appointments

RUTH W. CHABAY, Senior Research Scientist, Center for Innovation in Learning — Ph.D., University of Illinois, Urbana-Champaign; Carnegie Mellon, 1987—.

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

STEPHANIE TRISTRAM-NAGLE, Senior Research Biologist, Biological Sciences — Ph.D., University of California, Berkeley; Carnegie Mellon, 1982—.