## Syllabus

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.