Path integrals in curved spaces

David W. McLaughlin; L. S. Schulman

doi:10.1063/1.1665567

Path integrals in curved spaces

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we present a simplification of the path integral solution of the Schrödinger equation in terms of coordinates which need not be Cartesian. After presenting the existing formula, we discuss the relationship between the distance and time differentials. Making this relationship precise through the technique of stationary phase, we are able to simplify the path integral. The resulting expression can be used to obtain a Hamiltonian path Integral. Finally, we comment on a similar phenomenon involving differentials in the Itô integral.

Original language	English (US)
Pages (from-to)	2520-2524
Number of pages	5
Journal	Journal of Mathematical Physics
Volume	12
Issue number	12
DOIs	https://doi.org/10.1063/1.1665567
State	Published - 1971

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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