Complex time, contour independent path integrals, and barrier penetration

Research output: Contribution to journalArticle

Abstract

By developing an analogy between the Feynman path integral and contour integral representations of the special functions, we obtain WKB formulas for barrier penetration from a path integral. We first show that there exists for the path integral a notion of contour independence in the time parameter. We then select an appropriate contour to describe the physical situation of barrier penetration and obtain asymptotic formulas from the function space integral. The method is interpreted as a path integral derivation of the complex ray description of barrier penetration. In the last three sections we investigate several canonical problems of the theory of complex rays with these path integral techniques.

Original languageEnglish (US)
Pages (from-to)1099-1108
Number of pages10
JournalJournal of Mathematical Physics
Volume13
Issue number8
StatePublished - 1972

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Curvilinear integral
Penetration
penetration
Half line
Feynman Path Integral
Contour integral
Special Functions
Asymptotic Formula
Integral Representation
rays
Function Space
Analogy
function space
derivation

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

Complex time, contour independent path integrals, and barrier penetration. / McLaughlin, David W.

In: Journal of Mathematical Physics, Vol. 13, No. 8, 1972, p. 1099-1108.

Research output: Contribution to journalArticle

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