Path integral approach for spaces of nonconstant curvature in three dimensions
- Universitaet Hamburg, II. Institut fuer theoretische Physik (Germany), E-mail: Christian.Grosche@desy.de
In this contribution, I show that it is possible to construct three-dimensional spaces of nonconstant curvature, i.e., three-dimensional Darboux spaces. Two-dimensional Darboux spaces have been introduced by Kalnins et al., with a path integral approach by the present author. In comparison to two dimensions, in three dimensions it is necessary to add a curvature term in the Lagrangian in order that the quantum motion can be properly defined. Once this is done, it turns out that, in the two three-dimensional Darboux spaces which are discussed in this paper, the quantum motion is similar to the two-dimensional case. In D{sub 3d-I}, we find seven coordinate systems which separate the Schroedinger equation. For the second space, D{sub 3d-II}, all coordinate systems of flat three-dimensional Euclidean space which separate the Schroedinger equation also separate the Schroedinger equation in D{sub 3d-II}. I solve the path integral on D{sub 3d-I} in the (u, v, w) system and on D{sub 3d-II} in the (u, v, w) system and in spherical coordinates.
- OSTI ID:
- 21075917
- Journal Information:
- Physics of Atomic Nuclei, Vol. 70, Issue 3; Other Information: DOI: 10.1134/S1063778807030131; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
- Country of Publication:
- United States
- Language:
- English
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