Physics 613: Electrodynamics and Special Relativity

This course will be given during winter 2006 at the University of Calgary. Lectures will take place Monday, 11:00-12:15am and Tuesday, 3:30-4:45pm in SS 115 (Social Science).

This is a graduate course held during winter 2006 at the University of Calgary. The course is based on lecture notes. You may also download an incomplete German version of the lecture notes. In addition, participants may consider to get the book Classical Electrodynamics by J.D. Jackson.

The final exam will be held on Monday, April 17, from 12:00-2:00pm in SS 105.

Preliminary Table of Contents of Lecture Notes

  1. Maxwell equations and gauge transformations
    1. Maxwell equations
    2. Basic facts about linear differential equations
    3. Scalar and vector potential
    4. Gauge transformations
    5. Interaction with charged particles
    6. Energy- and momentum density

  2. Electrostatics
    1. Coulomb potential, Poisson and Laplace equations
    2. Green's functions
    3. Boundary conditions, Green's theorem
    4. The method of mirror charges
    5. Green's functions in spherical coordinates

  3. Magnetostatics
    1. Field equations and their solutions
    2. The law of Biot and Savart
    3. Magnetic quadrupole traps

  4. Dynamical fields
    1. Plane waves
    2. Green's functions
    3. Liénard-Wiechert potentials
    4. Multipole expansion
      1. Scalar multipoles
      2. Multipole expansion for vector fields

  5. Electrodynamics in dielectric media
    1. Macroscopic Maxwell equations
    2. Continuity relations at boundaries between two dielectrics
    3. Electrostatic problems in dielectric media
    4. Clausius-Mosotti and Lorentz-Lorenz relations
    5. Magnetized media

  6. Linear and nonlinear optics
    1. Reflection and refraction
      1. Total reflection
    2. Birefringence and optical activity
    3. Eikonal approximation, geometric optics
    4. Paraxial approximation and focused light beams
    5. Nonlinear optics
      1. Example 1: harmonic generation
      2. Example 2: Solitons

  7. Special relativity
    1. Form invariance of dynamical equations, Galilei transformations
    2. Einstein's postulates, Lorentz transformations
    3. Length contraction and time dilation
    4. Lorentz group and tensors
    5. Electrodynamics in relativistic notation
    6. Proper time and relativistic mechanics
    7. Paradoxes
      1. Twin paradox
      2. The barn pole paradox
      3. How a moving object is perceived

  8. A glimpse beyond this course
    1. General relativity
    2. Quantum electrodynamics

  9. Useful equations
    1. Calculations involving the δ distribution and Kronecker's symbol
    2. Gradient, curl, and all that
      1. Vector identities
      2. Laplace operator in spherical coordinates
    3. Integral theorems
      1. Gauss' theorem
      2. Stokes' theorem
      3. Green's integral identities

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