Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

Details Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

1999-04-29

arxiv.org/abs/quant-ph/9904103v2

Physics

Quantum Physics

5 pages, to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.60.1698

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.

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