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Path Integral Discussion for Smorodinsky‐Winternitz Potentials: II. The Two‐ and Three‐Dimensional Sphere
Author(s) -
Grosche C.,
Pogosyan G. S.,
Sissakian A. N.
Publication year - 1995
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190430603
Subject(s) - path integral formulation , propagator , functional integration , curvature , integrable system , integral equation , coordinate system , mathematics , mathematical analysis , line integral , physics , mathematical physics , geometry , quantum , quantum mechanics
Steps towards path integral formulations for Smorodinsky‐Winternitz potentials, respectively systems with accidental degeneracies, on the two‐ and three‐dimensional sphere, and a complete classification of super‐integrable systems on spaces of constant curvature are presented. We mention all coordinate systems which separate the Smorodinsky‐Winternitz potentials on a sphere, and state the corresponding path integral formulations. Whereas in many coordinate systems explicit path integral solutions are not possible, we list in all soluble cases the path integral in terms of the propagator, respectively the spectral expansion into the wave functions and the energy spectrum.