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The
Basic Physics Exam Requirement
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
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