1. Classical Principles of Electromagnetism
Electric ( ) and magnetic field ( ) are caused by electric charges (e-) and derive from the same underlying vector field
Maxwell Equations
s.i. units
Charged particle (charge e, velocity ) in elm field e
Int Elm Rad
Force F with inertia (m) and initial conditions determine classical trajectory of particle. QM task: Develop theory consistent with measurement
W. Udo Schröder, 20018

2. Classical Principles of Electromagnetism
Electric ( ) and magnetic field ( ) are caused by electric charges (e-) and derive from the same underlying vector field
Maxwell Equations c.g.s. units
Charged particle (charge e, velocity ) in elm field e
Int Elm Rad
Force F with inertia (m) and initial conditions determine classical trajectory of particle. QM task: Develop theory consistent with measurement
W. Udo Schröder, 20018

3. QM: Charged-Particle Coupling to Elm Field
Int Elm Rad
Larger task: Derive an internally consistent quantum mechanical account of the properties of field quanta and interactions with particles.
W. Udo Schröder, 20018

4. Charged Particles in Elm Fields
Explain, or model, Lorentz force on particle (mass m, charge e): Non-conservative, velocity (v) dependent force  effective potential
Int Elm Rad
W. Udo Schröder, 20018

5. Minimum Coupling to Field
Schrödinger Equation for charged (e) particle in elm field
Int Elm Rad
W. Udo Schröder, 20018

6. 1st Order Interaction Hamiltonian
First term is kinetic energy of free, unperturbed particle. Last term is of second order in field A, neglect in first order estimate.
Int Elm Rad
Interaction Hamiltonian of particle (mass m, charge q, magnetic moment m) with time dependent elm. field Add ad hoc spin magnetic interaction
Make real by adding complex conjugate CC.
Larmor frequency.
W. Udo Schröder, 20018

7. More Degrees of Freedom
Int Elm Rad
Since mp ≈2000·me, electronic terms are dominant for atoms and molecules.
W. Udo Schröder, 20018

8. Application in Perturbation Theory
Interaction Hamiltonian of particle (mass m, charge q, magnetic moment m) with time dependent elm. field
Use in perturbation theory, single-photon emission or absorption
Int Elm Rad
W. Udo Schröder, 20018

9. Hint with spin and orbital mu
Int Elm Rad
W. Udo Schröder, 20018