Physics 4322

Advanced Topics
Physics 4322 Syllabus

Part I: Modern Introductory Mechanics

Chapter 8: The Two Body Central Force Problem

Relative coordinates
Runge-Lenz treatment of Coulomb force
Lagrangian equations of motion
Celestial mechanics
General Relativity modification
Orbital stability 
Virial theorem

Chapter 9: Scattering and Collisions of Particles

Multi-particle conservation laws
Coulomb scattering
Differential cross sections
Rutherford scattering in the center of mass frame
Simple treatment of light deflection
Cross section cookbook
Connection between Lab and CM frames
A kinematical example in the Lab frame
Rutherford scattering in the laboratory frame
Total cross section

Chapter 10: Non inertial Reference Frames

Finite displacements and rotations
Instantaneous relations for velocity, acceleration
Useful Earth coordinate choices
Deflection of projectiles near Earth¹s surface
Deflections for dropped objects
Focault pendulum

Chapter 11: Rigid Body Motion

Concept of a rigid body
Instantaneous kinetic energy in body frame
Angular momentum and the inertia tensor
Transformation properties of the inertia tensor
Principal axes
Parallel axis theorem
Euler angles
Euler¹s equations of motion
Symmetrical top ­ Euler solution
Symmetrical top ­ Lagrangian solution

Chapter 12: Coupled Oscillations

Coupled dynamical equations
Eigenvalue/eigenvector solution
Weak/strong coupling
Example using mechanical/electrical analogy

Chapter 13: Special Relativity

Invariance and covariance
Two postulates of special relativity
Lorentz tranformations deduced
Alternate notation for Lorentz transformations
The ³light cone² and tachyons
Mathematical properties of Lorentz transformations
Consequences of relativity
Velocity addition law
Momentum and energy united
Four short points

Part II: Electrodynamics

Chapter 1: Electromagnetic Waves

The Wave Equation in One Dimension
One Dimensional Scattering
Two Dimensional Scattering
Electromagnetic Plane Waves
Electromagnetic Scattering – Nonconducting Case
Electromagnetic Scattering – Conducting Case
Model of Constuitive Relations for Nonconductors
Wave Guides

Chapter 2: Potentials and Fields

Potential formulation
Gauge transformations
Retarded potentials
Point particle fields
Moving point particle field example

Chapter 3: Radiation

Arbitrary source radiation
Multipole expansion
Electric and magnetic multipole results
Lienard result and circular accelerators