Path integral solution of the Schr{umlt o}dinger equation in curvilinear coordinates: A straightforward procedure
- Department of Physics and Center for Relativity, University of Texas, Austin, Texas 78712 (United States)
A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schr{umlt o}dinger 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 {open_quote}{open_quote}quantum corrections{close_quote}{close_quote} 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 Schr{umlt o}dinger equation is straightforward. The case of the Schr{umlt o}dinger equation in spherical coordinates for a free particle is presented in detail. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 286923
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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