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

Zaida Ann Luthey-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

Fingerprint

double precision arithmetic
evaluation
Wave functions
Derivatives
expansion
approximation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

A numerical algorithm for the evaluation of Weber parabolic cylinder functions U(a,x), V(a,x), and W(a, ±x). / Luthey-Schulten, Zaida Ann; Gordon, R. G.; Anderson, D. G M.

In: Journal of Computational Physics, Vol. 42, No. 2, 08.1981, p. 213-237.

Research output: Contribution to journalArticle

@article{d22c98bfb6214a739ccefc4bda9891fa,
title = "A numerical algorithm for the evaluation of Weber parabolic cylinder functions U(a,x), V(a,x), and W(a, ±x)",
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.",
author = "Luthey-Schulten, {Zaida Ann} and Gordon, {R. G.} and Anderson, {D. G M}",
year = "1981",
month = "8",
doi = "10.1016/0021-9991(81)90241-2",
language = "English (US)",
volume = "42",
pages = "213--237",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - A numerical algorithm for the evaluation of Weber parabolic cylinder functions U(a,x), V(a,x), and W(a, ±x)

AU - Luthey-Schulten, Zaida Ann

AU - Gordon, R. G.

AU - Anderson, D. G M

PY - 1981/8

Y1 - 1981/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3042936940&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042936940&partnerID=8YFLogxK

U2 - 10.1016/0021-9991(81)90241-2

DO - 10.1016/0021-9991(81)90241-2

M3 - Article

AN - SCOPUS:3042936940

VL - 42

SP - 213

EP - 237

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -