dorsal/arxiv
View SchemaSUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra
| Authors | A. A. Andrianov, F. Cannata, J. -P. Dedonder, M. V. Ioffe |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806019 |
| URL | https://arxiv.org/abs/quant-ph/9806019 |
| DOI | 10.1142/S0217751X99001342 |
| Journal | Int.J.Mod.Phys. A14 (1999) 2675-2688 |
Abstract
We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study in general the isospectrality between complex potentials. In very specific cases we can construct in a natural way "quasi-complex" potentials which we define as complex potentials having a global property such as to lead to a Hamiltonian with real spectrum. We also obtained a class of complex transparent potentials whose Hamiltonian can be intertwined to a free Hamiltonian. We provide a variety of examples both for the radial problem (half axis) and for the standard one-dimensional problem (the whole axis), including remarks concerning scattering problems.
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"abstract": "We extend the standard intertwining relations used in Supersymmetrical (SUSY)\nQuantum Mechanics which involve real superpotentials to complex\nsuperpotentials. This allows to deal with a large class of non-hermitean\nHamiltonians and to study in general the isospectrality between complex\npotentials. In very specific cases we can construct in a natural way\n\"quasi-complex\" potentials which we define as complex potentials having a\nglobal property such as to lead to a Hamiltonian with real spectrum. We also\nobtained a class of complex transparent potentials whose Hamiltonian can be\nintertwined to a free Hamiltonian. We provide a variety of examples both for\nthe radial problem (half axis) and for the standard one-dimensional problem\n(the whole axis), including remarks concerning scattering problems.",
"arxiv_id": "quant-ph/9806019",
"authors": [
"A. A. Andrianov",
"F. Cannata",
"J. -P. Dedonder",
"M. V. Ioffe"
],
"categories": [
"quant-ph",
"hep-th",
"nlin.SI",
"solv-int"
],
"doi": "10.1142/S0217751X99001342",
"journal_ref": "Int.J.Mod.Phys. A14 (1999) 2675-2688",
"title": "SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra",
"url": "https://arxiv.org/abs/quant-ph/9806019"
},
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