A numerical algorithm for the evaluation of Weber parabolic cylinder functions U(a,x), V(a,x), and W(a, ±x)

Z. Schulten, R. G. Gordon, D. G.M. Anderson

Research output: Contribution to journalArticle

Abstract

Weber's parabolic, cylinder functions U(a, x), V(a, x), and W(a, ±x) have recently found wide applications as approximations to quantum mechanical and semi-classical wavefunctions propagating through potential wells or barriers. Available algorithms for their numerical evaluation are inapplicable in some ranges of the two arguments. In this paper we present a, new algorithm, based on the combined use of F. W. J. Olver's (J. Res. Nat. Bur. Stand. Sect. B 63 (1959), 131) uniform asymptotic expansions and E. T. Whittaker's (Proc. London Math. Soc. 35 (1903), 417) complex recurrence relations, to extend their range of usefulness. Using double precision arithmetic, the algorithm generates greater than single precision values of the functions and their derivatives on a Univac 1182.

Original languageEnglish (US)
Pages (from-to)213-237
Number of pages25
JournalJournal of Computational Physics
Volume42
Issue number2
DOIs
StatePublished - Aug 1981
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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