Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV

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dc.creatorGrosche, Christian
dc.creatorPogosyan, George
dc.creatorSissakian, Alexei
dc.date2006-09-07
dc.date.accessioned2026-07-07T11:07:46Z
dc.date.available2026-07-07T11:07:46Z
dc.descriptionThis is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces $\DIII$ and $\DIV$ five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively.
dc.identifierhttps://arxiv.org/abs/quant-ph/0609058
dc.identifierhttp://arxiv.org/abs/quant-ph/0609058
dc.identifierPhys.Part.Nucl.38:525-563,2007
dc.identifierdoi:10.1134/S1063779607050012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189956
dc.subjectQuantum Physics
dc.titlePath Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV
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