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
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