dorsal/arxiv
View SchemaPhase equivalent potentials, Complex coordinates and Supersymmetric Quantum Mechanics
| Authors | C. V. Sukumar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611012 |
| URL | https://arxiv.org/abs/quant-ph/0611012 |
| DOI | 10.1088/0305-4470/39/46/017 |
| Journal | J.Phys. A: Math. Gen. 39 (2006) 14499-14509 |
Abstract
Supersymmetric Quantum Mechanics may be used to construct reflectionless potentials and phase-equivalent potentials. The exactly solvable case of the $\lambda sech^2$ potential is used to show that for certain values of the strength $\lambda$ the phase-equivalent singular potential arising from the elimination of all the boundstates is identical to the original potential evaluated at a point shifted in the complex cordinate space. This equivalence has the consequence that certain general relations valid for reflectionless potentials and phase-equivalent potentials lead to hitherto unknown identities satisfied by the Associated Legendre functions. This exactly solvable probelm is used to demonstrate some aspects of scattering theory.
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"abstract": "Supersymmetric Quantum Mechanics may be used to construct reflectionless\npotentials and phase-equivalent potentials. The exactly solvable case of the\n$\\lambda sech^2$ potential is used to show that for certain values of the\nstrength $\\lambda$ the phase-equivalent singular potential arising from the\nelimination of all the boundstates is identical to the original potential\nevaluated at a point shifted in the complex cordinate space. This equivalence\nhas the consequence that certain general relations valid for reflectionless\npotentials and phase-equivalent potentials lead to hitherto unknown identities\nsatisfied by the Associated Legendre functions. This exactly solvable probelm\nis used to demonstrate some aspects of scattering theory.",
"arxiv_id": "quant-ph/0611012",
"authors": [
"C. V. Sukumar"
],
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"quant-ph"
],
"doi": "10.1088/0305-4470/39/46/017",
"journal_ref": "J.Phys. A: Math. Gen. 39 (2006) 14499-14509",
"title": "Phase equivalent potentials, Complex coordinates and Supersymmetric Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0611012"
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