Qualifying Exam

The Qualifying Examination is given once in the Fall semester and once in the Spring semester. Its purpose is to verify that PhD candidates have a thorough understanding of the basics of physics at the level of first-year graduate courses and are ready for more advanced study. The material covered on the exam will closely follow that given in the Physics Department’s first-year courses.

The examination is divided into two parts, one covering topics involving quantum mechanics and the other covering topics involving classical mechanics and mathematical methods of physics. There will also be one statistical physics problem in each part (quantum and non-quantum respectively). There may also be a problem in each part which overlaps multiple topics. There will be a total of six questions in each part.

Topics Covered

Electricity and Magnetism

(Sample text: Classical Electrodynamics, 3^rd Edition, by J.D. Jackson)

• Electrostatics and Magnetostatics
• Green functions
• Maxwell’s Equations; Vector and Scalar Potentials; Gauge Transformations; Boundary Conditions; Energy Conservation
• Plane Electromagnetic Waves; Polarization
• Waveguides
• Radiation from Sources
• Special Relativity
• Dynamics of Relativistic Particles and Electromagnetic Fields

Mathematical Methods

(Sample text: Mathematical Methods of Physics, by J. Matthews and R. Walker)

• Vector Spaces, Linear Operators and Matrices
• Complex Analysis
• Asymptotic Methods

Classical Mechanics

(Sample text: Course of Theoretical Physics: Mechanics, by L. Landau and E. Lifshitz)

• Generalized Co-ordinates & Lagrangian Mechanics
• Central Force Problems; Scattering
• Small Oscillations
• Hamiltonian Mechanics; Poisson Brackets

Quantum Mechanics

(Sample text: Quantum Mechanics, by E. Merzbacher)

• Schrödinger Equation
• Classical Limits
• Bound States and Scattering; Harmonic Oscillator
• Angular Momentum & Spin; Commutation Relations
• Hydrogen Atom
• Identical Particles and Statistics
• Central Potential Scattering; Partial Waves
• Perturbation; Time Dependent Perturbation; Fermi’s Golden Rule; Adiabatic Approximations
• Scattering theory
• Addition of Angular Momenta; Partial Waves
• Dirac Equation

Statistical Physics

(Sample text: Statistical Mechanics, 2^nd Edition, by R.K. Pathria)

• Postulates of statistical physics and thermodynamic equilibrium
• Microcanonical ensemble
• Canonical ensemble
• Grand canonical ensemble
• Quantum statistics
• Ideal Bose systems
• Ideal Fermi systems