Perturbation Theory

Phase 4: Approximation Methods & Atomic Theory

Syllabus Goal

Time-independent (Stark effect) and Time-dependent (transsitions) perturbation theory.

Time-Independent (Stationary)

$$ H = H_0 + \lambda H’ $$

• First Order Energy: $E_n^{(1)} = \langle \psi_n^0 | H’ | \psi_n^0 \rangle$.
• Correction: Expectation value of the perturbation in the unperturbed state.
• Example: Stark effect (shift in E-field).

Time-Dependent

Covers transitions between states (absorption/emission).

• Fermi’s Golden Rule: Transition rate $W_{i\to f} \propto |\langle f | H’ | i \rangle|^2 \rho(E_f)$.