Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two- and Three Dimensional Euclidean Space

Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimen\-sional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinat...

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Bibliographic Details
Published in:arXiv.org 1994-02
Main Authors: Grosche, C, Pogosyan, G S, Sissakian, A N
Format: Article
Language:English
Subjects:
Coordinates
Euclidean geometry
Euclidean space
Formulations
Integrals
Quantum theory
Online Access:Get full text
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Summary:Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimen\-sional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave-functions.
ISSN:2331-8422
DOI:10.48550/arxiv.9402121