### 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 |

State | Published - 1971 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*12*(12), 2520-2524.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 12, no. 12, pp. 2520-2524.

}

TY - JOUR

T1 - Path integrals in curved spaces

AU - McLaughlin, David W.

AU - Schulman, L. S.

PY - 1971

Y1 - 1971

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037916750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037916750&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0037916750

VL - 12

SP - 2520

EP - 2524

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

ER -