Path Integral Approach for Spaces of Non-constant Curvature in Three Dimensions
| dc.creator | Grosche, Christian | |
| dc.date | 2005-11-14 | |
| dc.date.accessioned | 2026-07-07T10:30:50Z | |
| dc.date.available | 2026-07-07T10:30:50Z | |
| dc.description | In this contribution I show that it is possible to construct three-dimensional spaces of non-constant 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 $\threedDI$ we find seven coordinate systems which separate the Schrödinger equation. For the second space, $\threedDII$, all coordinate systems of flat three-dimensional Euclidean space which separate the Schrödinger equation also separate the Schrödinger equation in $\threedDII$. I solve the path integral on $\threedDI$ in the $(u,v,w)$-system, and on $\threedDII$ in the $(u,v,w)$-system and in spherical coordinates. | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0511135 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0511135 | |
| dc.identifier | Phys.Atom.Nucl.70:537-544,2007 | |
| dc.identifier | doi:10.1134/S1063778807030131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/178259 | |
| dc.subject | Quantum Physics | |
| dc.title | Path Integral Approach for Spaces of Non-constant Curvature in Three Dimensions | |
| dc.type | text |