Collisions and umbilic catastrophes the hyperbolic umbilic canonical diffraction integral

T. Uzer, James Muckerman, M. S. Child

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Two procedures to evaluate the hyperbolic umbilic canonical diffraction integral, a function that occurs in many applications of semiclassical collision theory and optics, are described. The first is the integration of the various differential equations satisfied by this function. We present schemes to perform the numerical integration and investigate their range of validity. A second algorithm, which evaluates the integral directly by quadrature, is given'. Here, attention is focused on the very rapidly oscillating regions of the integrand. The direct quadrature method is shown to be more widely applicable and better suited to numerical computation.

Original languageEnglish
Pages (from-to)1215-1230
Number of pages16
JournalMolecular Physics
Volume50
Issue number6
DOIs
Publication statusPublished - 1983

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quadratures
Diffraction
collisions
numerical integration
diffraction
Optics
Differential equations
differential equations
optics

ASJC Scopus subject areas

  • Biophysics
  • Molecular Biology
  • Physical and Theoretical Chemistry
  • Condensed Matter Physics

Cite this

Collisions and umbilic catastrophes the hyperbolic umbilic canonical diffraction integral. / Uzer, T.; Muckerman, James; Child, M. S.

In: Molecular Physics, Vol. 50, No. 6, 1983, p. 1215-1230.

Research output: Contribution to journalArticle

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