Path integrals in curved spaces

David W. McLaughlin, L. S. Schulman

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2520-2524
Number of pages5
JournalJournal of Mathematical Physics
Volume12
Issue number12
StatePublished - 1971

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Hamiltonians
Curvilinear integral
Integral Solution
Stationary Phase
Hamiltonian path
Cartesian
Simplification
Simplify
simplification
Relationships

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

Path integrals in curved spaces. / McLaughlin, David W.; Schulman, L. S.

In: Journal of Mathematical Physics, Vol. 12, No. 12, 1971, p. 2520-2524.

Research output: Contribution to journalArticle

McLaughlin, DW & Schulman, LS 1971, 'Path integrals in curved spaces', Journal of Mathematical Physics, vol. 12, no. 12, pp. 2520-2524.
McLaughlin, David W. ; Schulman, L. S. / Path integrals in curved spaces. In: Journal of Mathematical Physics. 1971 ; Vol. 12, No. 12. pp. 2520-2524.
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