Core Graduate Courses

In May 1991, the Graduate Curriculum Revision Committee published an extensive report describing the current curriculum; this new curriculum was then passed by the general faculty. Each of the four core classes—Classical Mechanics (385K), Statistical Mechanics (385L), Electricity and Magnetism (387K), and Quantum Mechanics (389K)—is required to have a final exam, which is to count as 50% of the grade in the course. Each is also required to have a consistent syllabus that specifies the content of ~75% of the course, leaving an additional 25% of the topics to the discretion of the instructor. Each final exam is to be based upon the core material specified in the syllabus and not upon supplementary material. The exam must also be available to students attempting to pass the core requirement through the exam only. Supplemental material can influence the final grade through homework and mid-terms.

In 1991, the GSSC formed committees to generate the core syllabi. In the summer of 2009, the GSSC formed a subcommittee to revise these syllabi for current practice. Faculty are expected to adhere to these core syllabi to make clear to students what is expected of them. Textbooks are suggested for some of the courses, but the textbook selection is at the discretion of the instructor.

PHY 385K—Mechanics

Curriculum Committee: Wendell Horton (chair), Phil Morrison, and Herb Berk

Recent textbooks include J. Jose and E. Saletan, Classical Dynamics: A Contemporary Approach (Cambridge, 1998), with supplementary texts H. Goldstein, Charles Poole, and John Safko, Classical Mechanics, 3rd Ed. (Prentice Hall).

The course will cover Newton’s laws of motion, phase space, Lagrangians, Hamilton’s principle, scattering theory, chaotic scattering, Lyapunov exponents, linear and nonlinear oscillators, overlapping resonance, KAM theorem, integrability, Hamilton-Jacobi theory, action-angle variables, sympletic maps, and the Liouville theorems. Scientific computing is required for solving the nonlinear dynamics homework problems.

Instructors may draw 25% of the material from additional topics, which may include: Stormer orbits in dipole magnetic fields; geometrical formulation of mechanics in one and two forms; rigid body motion in Euler angles; action-angle variables for charged particle in general magnetic fields; light rays and wave packet trajectories in inhomogeneous media and/or lenses; stability of orbits in synchrotrons and other accelerators; orbits in high powered laser fields.

PHY 385L—Statistical Mechanics

Curriculum Committee: Qian Niu (chair), Allan MacDonald, and Michael Marder

A. The Laws of Thermodynamics (Concepts of equilibrium, temperature, heat, and entropy)

B. The rules of Equilibrium Statistical Mechanics (Ensembles, classical and quantum)

C. Elementary Applications of Ensemble theory (Ideal gases, Black-body radiation, Curie magnetism, etc.)

D. Interacting systems (Perturbation theory, Monte Carlo methods, phase transitions, critical phenomena)

E. Kinetics and Transport

PHY 387K—Electricity and Magnetism

Curriculum Committee: Mike Downer (Chair), Herb Berk, Gennady Shvets, Takeshi Udagawa, and Austin Gleeson

Textbook: J. D. Jackson, Classical Electrodynamics, 3rd ed.¹ Internet sites featuring solutions to Jackson’s problems have proliferated in recent years.² Those instructors who use Jackson’s problems for assignments should therefore establish through their course syllabi a clear policy regarding use of these sites, as well as clear grading procedures. These might include counting homework only a small percentage of the course grade, using an honor system, etc. Instructors should also be encouraged to draw on other sources for graded homework and exam problems.

Curriculum

Required: (i) Highlights of Chapters 1-5, treated as a review of electrostatics, magnetostatics, and mathematical techniques covered in most undergraduate E&M courses. (2 to 3 weeks)
(ii) Chapters 6-10. These chapters should be covered in depth through class lectures and discussion, homework assignments, mid-term exams, and the final exam with options as described below (11 to 12 weeks)

Optional: Individual instructors may, at their discretion… (i) …skip a small fraction (~¼ or less) of the sections of any of the core chapters 6 through 10.
(ii) …add selected material from later chapters of Jackson (e.g. relativistic theory of fields and particles) or from other sources (e.g. nonlinear optics) up to ~20% of the course content (~2 to 3 weeks). In this case, the instructor may elect to skip a larger fraction of chapters 8, 9, or 10. In no case should an entire chapter 6 through 10 be skipped.

The committee recognized that having only one required E&M core course entails omitting material from the core that some faculty and students consider vitally important. PHY 387L provides a natural home for this material. Instructors should not attempt to teach it in PHY 387K, except as noted above, because that contributes to inconsistency in the core curriculum.³

PHY 387L should be the Department’s primary venue for advanced instruction in relativistic theory of particles and fields (Jackson chapters 11–16) and other advanced E&M topics not covered in PHY 387K. Note that PHY 387L can substitute for PHY 387K as a core course requirement for students who have completed a prior Jackson-level E&M course.

Exams

When only a single section of PHY 387K is held, the norm for the past decade, the PHY 387K instructor is solely responsible for composing, grading, and setting procedural rules (e.g. open- vs. closed-book) for the final exam for both course enrollees and exam-only candidates.

If, in the future, two or more sections of PHY 387K are held simultaneously, a common final exam should be administered for all sections.

Course procedures and policies outside of the final exam should be left at the discretion of individual instructors. From recent practice, typical pre-final course requirements include two mid-term exams (or one mid-term and a term paper) and regular homework assignments.

Notes

¹ This updates the 1991 recommendation of Jackson’s 2nd ed. The committee discussed several alternative texts, including Brau, Modern Problems in Classical Electrodynamics (OUP 2004), which is used at Vanderbilt University; Landau & Lifschitz, The Classical Theory of Fields, 4th ed.; and Schwinger, Classical Electrodynamics. Some committee members were favorably impressed with Brau’s book, noting that it provides a multitude of new problems as potential alternatives to Jackson’s. In the end, however, we decided unanimously that Jackson’s text provides the best level of instruction for beginning graduate students and remains unrivaled in its breadth and depth of coverage. We noted that Jackson’s text is used by 76 of 80 graduate physics programs surveyed in the 2005 AIP report Core and Breadth in Physics Doctoral Education (Table 16).

² Some examples:
http://www-personal.umich.edu/~pran/jackson/
http://virgo.physics.ucdavis.edu/~tanya/jackson/jackson.html

³ In specifying this content, the committee was cognizant of a recommendation by the APS/AAPT Task Force on Graduate Education (TFGE) in its 2005 report Graduate Education in Physics “...that the content of core courses be consistent year-to-year and supervised closely by the department. Within that context, the TFGE believes that turnover in instructors is a good thing.” (p.12)

⁴ The committee noted from the 2005 APS/AAPT report that 26% of surveyed programs, like us, required a single E&M course, whereas 74% required two E&M courses. On the other hand, most top-30 departments, like us, required only a single E&M course.

PHY 389K—Quantum Mechanics

Curriculum Committee: Arno Bohm (chair), Duane Dicus, and Mark Raizen

Recent textbooks have included Modern Quantum Mechanics (Revised Ed.) by J. J. Sakurai and S. F. Tuan(Adison-Wesley); and Quantum Mechanics: Foundations and Applications by A. Bohm.

A. Introducing the basic ideas of quantum mechanics using 1-D systems (square well, harmonic oscillator)

B. Quantum mechanics in 3 dimensions, angular momentum, rotational systems and/or hydrogen atom

C. Combination of quantum systems: Center of mass and relative motion and/or other examples. Addition of angular momenta.

D. Time-independent perturbation theory, particles in an external magnetic fields

E. Time evolution of quantum systems

F. Fundamentals of scattering theory (if time permits)

Advanced Physics Courses

PT
396K—Quantum Field Theory I
396L—Quantum Field Theory II
396P—String Theory I
396Q—String Theory II

HE
396J—Intro. to Elementary Particle Physics

NU
397K—Intro. to High Energy Physics & RHIC

REL
387M—Relativity I
387N—Relativity II

ND
382M—Fluid Mechanics
382N—Nonlinear Mechanics
382P—Biophysics I
382Q—Biophysics II

PL
380L—Plasma Physics I
380M—Plasma Physics II

CM
392K—Solid State Physics I
392L—Solid State Physics II
392N—Many Body Theory

A&M
395—Atomic & Molecular Physics
395K—Nonlinear Optics and Lasers
395L—Laser Physics

THEORY
386K—Physics of Sensors

NON-SPECIAL^*:
387L—E&M II
389L—Quantum Mechanics II
381N—Advanced Method of Mathematical Physics

^* The courses under this category cannot be used as an advanced course outside your specialty. All other courses can be.

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