### 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 language | English (US) |
---|---|

Pages (from-to) | 1099-1108 |

Number of pages | 10 |

Journal | Journal of Mathematical Physics |

Volume | 13 |

Issue number | 8 |

State | Published - 1972 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 13, no. 8, pp. 1099-1108.

}

TY - JOUR

T1 - Complex time, contour independent path integrals, and barrier penetration

AU - McLaughlin, David W.

PY - 1972

Y1 - 1972

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36849102355&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849102355&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36849102355

VL - 13

SP - 1099

EP - 1108

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 8

ER -