The Basic Physics Exam Requirement - Exam I

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 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 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