WKB and Bohr-Sommerfeld quantization#
The classical momentum and turning points, the WKB wavefunction, and the Bohr-Sommerfeld (EBK) quantization rule, checked against the exact harmonic-oscillator spectrum and eigenstates; Weyl’s law counting levels by phase-space volume; Einstein’s torus quantization of the circular billiard; and the Langer correction that makes radial WKB exact for hydrogen.
Einstein’s torus quantization: the circular billiard
Einstein's torus quantization: the circular billiard
The Langer correction: exact hydrogen levels from radial WKB
The Langer correction: exact hydrogen levels from radial WKB
