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 (quals) 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.  It's really basic stuff, and you can't call yourself a PhD physicist without knowing it well.
 
 

Exam I (CP)- Mostly Classical Mechanics & Electrodynamics

Syllabus:

Classical Mechanics
    Conservation laws
    Central potential motion, especially Keplerian motion
    Simple harmonic
    Motion of charged particles in electromagnetic fields
    Normal modes and small oscillations
    Variational principles
    Euler equations
    Lagrangian and Hamiltonian formalisms
    Canonical transformations
    Rigid body motion
    Elastic and inelastic collisions

Electricity and Magnetism
    Electrostatics and magnetostatics
    Potentials
    Boundary-value problems, including simple conformal transformations
    Method of images
    Dipoles and Multipoles
    Fields in matter; E versus D, B versus H
    Maxwell's equations, formalism in terms of E, B, D, H, J, rho
    Oscillating fields
    Plane and spherical waves
    EM energy and momentum
    Reflection and refraction
    Radiation from accelerated point charges and oscillating dipoles
    Antennas
    Multipole radiation
    Waveguides and cavities
    Eddy currents
    Electric circuits: capacitance, inductance, resistance, generalized impedance

Special Relativity
    Lorentz transformations
    Four-vectors
    Relativistic mechanics
    Energy and momentum conservation in particle collisions, Compton scattering
    Transformations of electromagnetic fields

Basic Optics
    Fundamental geometrical optics
    Fundamental diffractive optics
    Michelson interferometers and Fabry-Perot cavities
    Basic physics of lasers

Basic Continuum Physics
    Elastostatics -- bulk modulus, shear modulus, Young's modulus, Poisson ratio
    Basic Hydrodynamics
    Bernoulli equation
    Navier-Stokes equation
    Basic shock waves

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
 

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