dorsal/arxiv
View SchemaPath Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV
| Authors | Christian Grosche, George Pogosyan, Alexei Sissakian |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609058 |
| URL | https://arxiv.org/abs/quant-ph/0609058 |
| DOI | 10.1134/S1063779607050012 |
| Journal | Phys.Part.Nucl.38:525-563,2007 |
Abstract
This 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.
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"abstract": "This is the second paper on the path integral approach of superintegrable\nsystems on Darboux spaces, spaces of non-constant curvature. We analyze in the\nspaces $\\DIII$ and $\\DIV$ five respectively four superintegrable potentials,\nwhich were first given by Kalnins et al. We are able to evaluate the path\nintegral in most of the separating coordinate systems, leading to expressions\nfor the Green functions, the discrete and continuous wave-functions, and the\ndiscrete energy-spectra. In some cases, however, the discrete spectrum cannot\nbe stated explicitly, because it is determined by a higher order polynomial\nequation.\n We show that also the free motion in Darboux space of type III can contain\nbound states, provided the boundary conditions are appropriate. We state the\nenergy spectrum and the wave-functions, respectively.",
"arxiv_id": "quant-ph/0609058",
"authors": [
"Christian Grosche",
"George Pogosyan",
"Alexei Sissakian"
],
"categories": [
"quant-ph"
],
"doi": "10.1134/S1063779607050012",
"journal_ref": "Phys.Part.Nucl.38:525-563,2007",
"title": "Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV",
"url": "https://arxiv.org/abs/quant-ph/0609058"
},
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