Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9604172 · Journal of Physics A Mathematical and General

Comment on path integral derivation of Schrödinger equation in spaces with curvature and torsion

P Fiziev, H Kleinert

Published Dec 7, 1996• 4 citations
arXivHTMLPDF

Abstract

We present a derivation of the Schrödinger equation for a path integral of a point particle in a space with curvature and torsion which is considerably shorter and more elegant than that commonly found in the literature.
DOI
10.1088/0305-4470/29/23/022

Related papers

Comment on Path Integral Derivation of Schrödinger Equation in Spaces with Curvature and Torsion

P. Fiziev, H. Kleinert

We present a derivation of the Schr odinger equation for a path integral of a point particle in a space with curvature and torsion which is considerably shorter and more elegant than that commonly found in the literature. 1.

•Jan 1, 1996•3 citations

Comment on: Path integral solution of the Schrödinger equation in curvilinear coordinates: A straightforward procedure [J. Math. Phys. 37, 4310–4319 (1996)]

Alexander Wurm, J. LaChapelle

The authors comment on the paper by J. LaChapelle, J. Math. Phys. 37, 4310 (1996), and give explicit expressions for the parametrization, its solution, and the Lie derivatives of the Schrödinger equation for the case of n-dimensional spherical coordinates.

Journal of Mathematical Physics•May 1, 1997•0 citations

Schrodinger Equation for Lagrangian Path Integral with Scaling of Local Time

Ashok Kumar Kapoor, Pankaj Sharan

A method for deriving the Schrodinger equation for Lagrangian path integral with scaling of local time is given.

arXiv:hep-th/9507081•Jul 14, 1995•0 citations

A derivation of the principles of canonical quantization

Howard E. Covington

Schrodinger's equation for a single particle is proved from the assumption that dynamics can be formulated in a space whose curvature is the electromagnetic force.

•Dec 8, 2009•0 citations

Path Integrals in Curved Spaces

David W. McLaughlin, Lawrence S. Schulman

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.

Journal of Mathematical Physics•Dec 1, 1971•136 citations

Path integral solution of the Schrödinger equation in curvilinear coordinates: A straightforward procedure

J. LaChapelle

A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schrödinger equation in curvilinear coordinates. An important feature of the formalism is that a coordinate transformation in the variables of the wavefunction does not imply a change of variable of integration in the path integral. Consequently, a transformation from Euclidean to curvilinear coordinates is simple to handle; there is no need to introduce ‘‘quantum corrections’’ into the action functional. Furthermore, the paths are differentiable: hence, issues related to stochastic paths do not arise. The procedure for constructing the path integral solution of the Schrödinger equation is straightforward. The case of the Schrödinger equation in spherical coordinates for a free particle is presented in detail.

Journal of Mathematical Physics•Sep 1, 1996•0 citations
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.
A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schrödinger equation in curvilinear coordinates. An important feature of the formalism is that a coordinate transformation in the variables of the wavefunction does not imply a change of variable of integration in the path integral. Consequently, a transformation from Euclidean to curvilinear coordinates is simple to handle; there is no need to introduce ‘‘quantum corrections’’ into the action functional. Furthermore, the paths are differentiable: hence, issues related to stochastic paths do not arise. The procedure for constructing the path integral solution of the Schrödinger equation is straightforward. The case of the Schrödinger equation in spherical coordinates for a free particle is presented in detail.