# 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
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