Interaction with Radiation

Phase 1: The Foundation

Syllabus Goal

Interaction of one-electron atoms with electromagnetic radiation. Derivations for electric dipole transitions and selection rules.

Electric Dipole Approximation

Interaction Hamiltonian: $$ H’ = -\mathbf{D} \cdot \mathbf{E} $$ where $\mathbf{D} = -e\mathbf{r}$ is the dipole moment.

Selection Rules

Transitions are only allowed if:

1. $\Delta \ell = \pm 1$
2. $\Delta m = 0, \pm 1$

Rates

• Fermi’s Golden Rule: Transition probability per unit time.
• Einstein Coefficients: $A$ (Spontaneous emission), $B$ (Stimulated emission/absorption).