## Course Descriptions

All students (except those who place out) must complete the following ten courses. Note that only written waivers are valid (email from instructor to Director of Graduate Study). Moreover, if a waiver is obtained, a different 400-level course must be taken. This must be a graded (i.e., not P/N) course. In addition to these ten courses, at least one more 400-level course must be taken before the end of the third year; typically this is an elective chosen in consultation with your research advisor. Many students choose more than one additional elective. Note that certain 300-level courses can be counted as a graduate-level course (please check with the Program Office).

**APP PHYS 501-1: Faculty Research Seminar** (Fall)

Seminars presented by faculty in the Applied Physics Graduate Program describing ongoing research.

**MAT SCI 401: Chemical & Statistical Thermodynamics of Materials** (Fall)

The following topics in classical thermodynamics will be covered: the laws of thermodynamics; conditions for equilibrium; solutions; excess quantities; binary and ternary phase diagrams. Additionally, the following topics in statistical thermodynamics will be covered: statistical definition of entropy; ensembles and the Boltzmann and Gibbs distributions; quantum and classical ideal gasses; and the regular solution model.

**PHYSICS 412-1,2: Quantum Mechanics** (Fall and Winter)

*First quarter*: Vector spaces and linear operators, postulates of quantum mechanics, observables and Hermitian operators, state vectors and quantum dynamics, stationary states, bound states, the harmonic oscillator, statistical interpretation and the Uncertainty Principle, symmetry and conservation laws, quantization of angular momentum, intrinsic spin, the Stern-Gerlach experiment, spherically symmetric potentials.

*Second quarter*: Feynman's path integral formulation, the classical limit, Schroedinger's wave equation, electromagnetic potentials, Aharonov-Bohm effects, Landau levels, Coulomb potential, approximation methods, variational principles, bound-state perturbation theory, Dirac's theory of the electron, electron spin, Dirac-Pauli equation, magnetic moment of the electron, fine structure of hydrogen, hyperfine interactions.

**PHYSICS 414-1: Electrodynamics** (Winter)

Electrostatics, boundary-value problems, Green's functions, multipoles, electrostatics of macroscopic media, conductors and dielectrics, magnetostatics, Maxwell's equations, electromagnetic waves and gauge transformations, conservation laws.

**PHYSICS 416-0: Introduction to Statistical Mechanics** (Winter)

Statistical mechanics and probability. Microstates and macrostates. Thermodynamic limit. Ensembles: microcanonical, canonical, grand canonical. Classical ideal gas: Maxwell-Boltzmann distribution. Quantum gases: Fermi-Dirac and Bose-Einstein distributions. Thermodynamic potentials. Interacting systems. Phase diagrams and phase transitions.

**PHYSICS 422-1: Condensed-Matter Physics** (Fall) (taken in the 2nd year)

Periodic potentials, crystal lattices, x-ray diffraction. Electrons in metals: Drude model, electrons in periodic potentials, semiclassical approximation, Fermi surface, band structure. Electronic and thermal transport, Boltzmann equation, electron-electron interactions, screening.

*or*

**MAT SCI 405: Physics of Solids** (Spring)

This course provides and overview of solid state physics including free electron theory, phonons, energy bands, charge transport, semiconductors, optical properties, dielectric properties, ferroelectrics, diamagnetism, paramagnetism, and magnetic ordering.

**Computational Methods of Applied Physics** (students choose a 400-level computational techniques course, with approval of the Director for Graduate Studies)

**Experimental Methods of Applied Physics** (students choose a 400-level laboratory techniques course, with approval of the Director for Graduate Studies)

**GEN ENG 519: Responsible Conduct of Research Training** (offered Fall, Winter, and Spring)

Should be taken in the first year. The goal of Responsible Conduct of Research (RCR) training is for anyone involved in research to perform the most ethical research possible. Northwestern University has in place a number of policies that clearly demonstrate our commitment to research integrity. Collectively, these apply to all members of Northwestern's research enterprise: students/trainees, staff and faculty.