### 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 language | English (US) |
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Pages (from-to) | 213-237 |

Number of pages | 25 |

Journal | Journal of Computational Physics |

Volume | 42 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1981 |

Externally published | Yes |

### 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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## Cite this

*Journal of Computational Physics*,

*42*(2), 213-237. https://doi.org/10.1016/0021-9991(81)90241-2