Syllabus for the qualifying exam:

You can expect questions about any material covered in an introductory physics text.  You can expect questions on advanced undergraduate physics concerning the topics listed below.

• CLASSICAL MECHANICS
  • Newton's Second Law of Motion
  • Some Commonly Encountered Forces
  • Impulsive Forces
  • Conservation of Linear Momentum, Angular Momentum and Mechanical Energy
  • Collisions Between Particles
  • Problems in which the Motion is Specified and the Forces must be Determined
  • Use of Non-inertial Reference Frames
  • Principal Axes 
  • Lagrange's and Hamilton's Equations for a Conservative System
  • Normal Mode Analysis of Small Oscillations about Equilibrium
  • Motion of a Particle in a Central Potential
  • Motion of a Particle in a 1/r Potential          
  • Relative and Center-of-Mass Coordinates
  • Mechanical Waves

• SPECIAL RELATIVITY
  • Lorentz Transformations in one Spatial Dimension
  • Time Dilation
  • Lorentz Contraction
  • Lorentz Transformation of Velocity and Acceleration
  • Momentum and Energy
  • The Doppler Shift
  • Collisions

• ELECTRICITY AND MAGNETISM
  • Maxwell's Equations and the Boundary Conditions on E and B
  • Electrostatics
  • Solving Problems Using the Uniqueness Theorems of Electrostatics
  • Maxwell's Equations in the Presence of Material Media
  • Ohm's Law and DC Circuits
  • AC Circuits with Harmonic Driving Voltage
  • Power Consumption in AC Circuits
  • Permanent Magnets
  • Magnetic Fields Produced by Free, Time-Independent Currents
  • The Lorentz Force
  • Potentials in Time-Dependent Situations
  • Lenz's Law
  • Energy and Momentum Densities and Flux
  • Inductance
  • Lorentz Transformations of the E and B Fields
  • Plane Wave Solutions of Maxwell's Equations in a Homogeneous Non-conducting Isotropic Medium
  • Simple Microscopic Models of Electrical Conductivity and Index of Refraction
  • Plane waves at interfaces
  • Electromagnetic Waves in Cavities and Pipes Within Perfect Conductors
  • Radiation by Non-relativistic Accelerating Charges

• QUANTUM MECHANICS
  • Classical Mechanics vs. Quantum Mechanics
  • The Formalism of Quantum Mechanics
  • Angular Momentum
  • Bound State Solutions of the One-Particle Schroedinger Equation
  • Density of States
  • Approximation Methods
  • Non-relativistic Charged Particle in an Electromagnetic Field
  • Time-Dependent Problems
  • Scattering in One Dimension by a Localized Potential
  • Scattering by a Three-Dimensional Localized Potential
  • Born Approximation

The book, "A REVIEW OF UNDERGRADUATE PHYSICS", presents a clear summary of most of the material covered in an American undergraduate program in physics.

A REVIEW OF UNDERGRADUATE PHYSICS
BENJAMIN F. BAYMAN, University of Minnesota
MORTON HAMERMESH, University of Minnesota
JOHN WILEY & SONS

Links to solved problems:

• Physics Problems