Perturbation Theory in Atomic Physics: Non-Degenerate and Degenerate Cases, Study notes of Physics

Download Perturbation Theory in Atomic Physics: Non-Degenerate and Degenerate Cases and more Study notes Physics in PDF only on Docsity! Lecture 38 Outline - Still Perturbed • time-independent perturbation theory: • (non-degenerate) Perturbation theory [Chapter 6.1.1] • First- and second-order theory [Chapter 6.1.2/6.1.3] • (degenerate) Perturbation theory [Chapter 6.2] • (briefly) Hydrogen fine structure [Chapter 6.3] • (very briefly) Zeeman/Stark effects [Chapter 6.4] Non-degenerate perturbation theory • Summary of formulae for time-independent potentials: En ≈ E 0 n + E 1 n E 1 n = 〈ψ 0 n|H ′|ψ0n〉 |ψn〉 ≈ |ψ 0 n〉 + |ψ 1 n〉 |ψ 1 n〉 = ∑ m6=n 〈ψ0m|H ′|ψ0n〉 (E0n − E 0 m) |ψ0m〉 • But how to know how accurate the solution really is? • Mosttimes compare with 2nd-order energy correction En ≈ E 0 n + E 1 n + E 2 n E 2 n = ∑ m6=n |〈ψ0m|H ′|ψ0n〉| 2 (E0n − E 0 m) • Rerun Problem 6.1, run through 6.4 (and then 6.2). • Obvious problem if we have degenerative energy levels...