The Basic Physics Exam Requirement - Exam II

The Basic Physics Exam Requirement II

General philosophy --

The Basic Physics Exam Requirement is meant to make sure you have a solid understanding of the fundamentals of physics -- classical mechanics, electricity and magnetism, quantum mechanics, statistical mechanics, basic optics and continuum physics, basic mathematical methods of physics, and the physics of everyday phenomena. This is generally undergraduate material, and most students have seen a lot of it before. No coursework is required, but you must pass two written candicacy examinations to qualify for admission to candidacy for the Degree of Doctor of Philosophy in Physics. The real point of the exams is to force you to study this material again, to absorb it more deeply than you did as an undergraduate.

Exam II (QM) - Mostly Quantum & Statistical Mechanics

Syllabus: 

Quantum Mechanics 
    Wave mechanics 
    Schroedinger equation 
    Matrix formulation 
    Dirac notation 
    Density matrix 
    Harmonic oscillator 
    Hydrogen atom 
    Basic symmetries (translation, reflection, rotation) and conservation laws 
    Rotations 
    Angular momentum and the addition of angular momentum 
    Spin and Pauli spin matrices 
    Wigner Eckart theorem 
    Basic scattering theory (including phase shifts and Born approximation) 
    Time-independent and time-dependent perturbation theory 
    Interaction of radiation with atoms and other systems 
    Identical particles 
    Zeeman and Stark effects 
    Quantum statistical mechanics -- Bose-Einstein and Fermi-Dirac statistics 
    Interaction of light with atoms 
    Basic NMR 
    Basic molecular physics

Statistical Physics 
    Basic kinetic theory 
    Systems, ensembles, and distribution functions 
    Phase space and the number density of quantum states in phase space 
    The black-body spectrum 
    Bose and Fermi statistics; degenerate matter 
    Entropy 
    Thermodynamic potentials: energy, enthalpy, etc. 
    Osmotic pressure 
    Specific heats of simple gases and solids 
    Basic first and second order phase transitions 
    Everything about ideal gases 
    Single-particle distribution function, Boltzmann equation 
    Basic theory of random processes 
    Langevin equation 
    Fluctuation-dissipation theorem (Nyquist theorem) 
    Brownian motion 
    The Chandrasehkar limit for white dwarf stars

Common to both exams: 
Mathematical Methods of Physics: 
    Analytic functions 
    Linear Spaces 
    Contour integration 
    Ordinary and partial differential equations 
    Integral transforms 
    Orthogonal polynomials 
    Eigenvalue problems 
    Fourier and spectral analysis 
    Statistics and Probability 
Physical Origin of Everyday Phenomena