Use of the WKB method for obtaining energy eigenvalues

J. B. Krieger, M. L. Lewis, Carl Rosenzweig

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

A simple, general method is derived for evaluating the second- and third-order WKB energy integrals by rewriting the integrals having nonintegrable singularities in terms of derivatives, with respect to the energy, of integrals having integrable singularities. As an example, it is shown that the higher-order WKB integrals vanish for the one-dimensional linear harmonic oscillator. A calculation of some eigenvalues using this method is made for potentials of the form V(x)=λx 2y and the results are compared to the "exact" results obtained from a numerical integration of the Schrödinger equation. It is observed that inclusion of the third-order integral improves the accuracy of WKB eigenvalues.

Original languageEnglish (US)
Pages (from-to)2942-2945
Number of pages4
JournalThe Journal of Chemical Physics
Volume47
Issue number8
StatePublished - 1967
Externally publishedYes

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eigenvalues
Derivatives
energy
numerical integration
harmonic oscillators
inclusions

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Krieger, J. B., Lewis, M. L., & Rosenzweig, C. (1967). Use of the WKB method for obtaining energy eigenvalues. The Journal of Chemical Physics, 47(8), 2942-2945.

Use of the WKB method for obtaining energy eigenvalues. / Krieger, J. B.; Lewis, M. L.; Rosenzweig, Carl.

In: The Journal of Chemical Physics, Vol. 47, No. 8, 1967, p. 2942-2945.

Research output: Contribution to journalArticle

Krieger, JB, Lewis, ML & Rosenzweig, C 1967, 'Use of the WKB method for obtaining energy eigenvalues', The Journal of Chemical Physics, vol. 47, no. 8, pp. 2942-2945.
Krieger JB, Lewis ML, Rosenzweig C. Use of the WKB method for obtaining energy eigenvalues. The Journal of Chemical Physics. 1967;47(8):2942-2945.
Krieger, J. B. ; Lewis, M. L. ; Rosenzweig, Carl. / Use of the WKB method for obtaining energy eigenvalues. In: The Journal of Chemical Physics. 1967 ; Vol. 47, No. 8. pp. 2942-2945.
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