Application of a higher-order WKB approximation to radial problems

J. B. Krieger, Carl Rosenzweig

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Abstract

The radial generalization of Dunham's one-dimensional WKB quantization condition, including second- and third-order corrections is derived using the Langer transformation. It is found that, although the first-order integral can be obtained from Dunham's results by substituting (l=12)2 for l(l+1) in the effective potential, there is no choice of effective potential that leads to the correct second- and third-order integrals. It is suggested that all previous eigenvalue calculations using higher-order WKB approximations for the radial case should be reinvestigated. It is shown that the second- and third-order integrals identically vanish for the hydrogen atom and the three-dimensional harmonic oscillator, as expected.

Original languageEnglish (US)
Pages (from-to)171-173
Number of pages3
JournalPhysical Review
Volume164
Issue number1
DOIs
StatePublished - 1967
Externally publishedYes

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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