Complex time, contour independent path integrals, and barrier penetration

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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
Pages (from-to)1099-1108
Number of pages10
JournalJournal of Mathematical Physics
Issue number8
StatePublished - 1972
Externally publishedYes


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