Theorem: Bohr-Sommerfeld quantization gives exact E_n = hbaromega(n + 1/2) for harmonic oscillator

Layer 1 — Physicsin the perturbation-theory subtree

Theorem (WKB Bohr-Sommerfeld exactness on harmonic oscillator): for the classical action of a 1D harmonic oscillator V(q) = (1/2) m*omega^2*q^2, the contour integral oint p dq over one period (energy-E ellipse in phase space) evaluates to…

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WKB semiclassical expansion: psi(x) ~ A(x)*exp(i*S(x)/hbar) with S expanded in powers of hbar

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