Electrons in an Electromagnetic Field

In this section, we will study the interactions of electrons in an electromagnetic field. We will compute the additions to the Hamiltonian for magnetic fields. The gauge symmetry exhibited in electromagnetism will be examined in quantum mechanics. We will show that a symmetry allowing us to change the phase of the electron wave function requires the existence of EM interactions (with the gauge symmetry).

These topics are covered in **Gasiorowicz Chapter 13,**
and in **Cohen-Tannoudji et al. Complements , and .**

- Review of the Classical Equations of Electricity and Magnetism in CGS Units
- The Quantum Hamiltonian Including a B-field
- Gauge Symmetry in Quantum Mechanics
- Examples

- Derivations and Computations
- Deriving Maxwell's Equations for the Potentials
- The Lorentz Force from the Classical Hamiltonian
- The Hamiltonian in terms of B
- The Size of the B field Terms in Atoms
- Energy States of Electrons in a Plasma I
- Energy States of Electrons in a Plasma II
- A Hamiltonian Invariant Under Wavefunction Phase (or Gauge) Transformations
- Magnetic Flux Quantization from Gauge Symmetry

- Homework Problems
- Sample Test Problems

Jim Branson 2013-04-22