Quantum Mechanics · Chapter 21

Charged particles in electromagnetic fields

How a charge enters quantum mechanics: through potentials rather than forces. Minimal coupling, gauge transformations as a change of phase, the Aharonov–Bohm effect of a field the particle never touches, Landau levels, magnetic moments and the Pauli Hamiltonian, the Zeeman effect, and diamagnetism and paramagnetism.

p^\mapsto p^- q A

H^= \frac{( p ^ - q A ) ^{2}}{2 m} + q ϕ

B = \nabla \times A

Δ φ = \frac{q Φ}{ℏ}

Lessons

Build the foundation

Diamagnetism and paramagnetismBring a strong magnet near most materials and nothing seems to happen, but a sensitive balance shows a tiny push.

Read lesson →

08Chapter practiceBring the chapter together: minimal coupling, gauge transformations, the Aharonov–Bohm effect, Landau levels, magnetic moments and the Pauli Hamiltonian, the Zeeman effect, and the magnetism of atoms. No worked example sits above the answers.Read lesson →

Mapping the lesson.

Charged particles in electromagnetic fields

Build the foundation