Application of a higher-order WKB approximation to radial problems

J. B. Krieger, Carl Rosenzweig

Research output: Contribution to journalArticle

41 Citations (Scopus)

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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Wentzel-Kramer-Brillouin method
harmonic oscillators
hydrogen atoms
eigenvalues

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Application of a higher-order WKB approximation to radial problems. / Krieger, J. B.; Rosenzweig, Carl.

In: Physical Review, Vol. 164, No. 1, 1967, p. 171-173.

Research output: Contribution to journalArticle

Krieger, J. B. ; Rosenzweig, Carl. / Application of a higher-order WKB approximation to radial problems. In: Physical Review. 1967 ; Vol. 164, No. 1. pp. 171-173.
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