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

Layer 1 — Physicsin the perturbation-theory subtree

Wentzel-Kramers-Brillouin (WKB) semiclassical expansion. Setup: stationary 1D Schrodinger equation -hbar^2/(2m) psi'' + V(x) psi = E psi. Ansatz psi(x) = exp(i S(x)/hbar) with S expanded in powers of hbar: S = S_0 + hbar S_1 + hbar^2 S_2 +…

Related concepts

Radius of convergence
Theorem: Bohr-Sommerfeld quantization gives exact E_n = hbar*omega*(n + 1/2) for harmonic oscillator

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