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

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

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

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

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

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

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

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

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