dorsal/arxiv
View SchemaDiscrete supersymmetries of the Schrodinger equation and non-local exactly solvable potentials
| Authors | Boris F. Samsonov, A. A. Suzko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301109 |
| URL | https://arxiv.org/abs/quant-ph/0301109 |
| DOI | 10.1016/S0375-9601(02)01145-3 |
| Journal | Phys. Lett. A 302 (2002) 234-241 |
Abstract
Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term difference equation. Technique of intertwining operators is applied to creating new families of exactly solvable Jacobi matrices. It is shown that any thus obtained Jacobi matrix gives rise to a new exactly solvable non-local potential of the Schroedinger equation. We also show that the algebraic structure underlying our approach corresponds to supersymmetry. Supercharge operators acting in the space $\ell^{2}\times \ell^{2} $ are introduced which together with a matrix form of the superhamiltonian close the simplest superalgebra.
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"abstract": "Using an isomorphism between Hilbert spaces $L^2$ and $\\ell^{2}$ we consider\nHamiltonians which have tridiagonal matrix representations (Jacobi matrices) in\na discrete basis and an eigenvalue problem is reduced to solving a three term\ndifference equation. Technique of intertwining operators is applied to creating\nnew families of exactly solvable Jacobi matrices. It is shown that any thus\nobtained Jacobi matrix gives rise to a new exactly solvable non-local potential\nof the Schroedinger equation. We also show that the algebraic structure\nunderlying our approach corresponds to supersymmetry. Supercharge operators\nacting in the space $\\ell^{2}\\times \\ell^{2} $ are introduced which together\nwith a matrix form of the superhamiltonian close the simplest superalgebra.",
"arxiv_id": "quant-ph/0301109",
"authors": [
"Boris F. Samsonov",
"A. A. Suzko"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0375-9601(02)01145-3",
"journal_ref": "Phys. Lett. A 302 (2002) 234-241",
"title": "Discrete supersymmetries of the Schrodinger equation and non-local exactly solvable potentials",
"url": "https://arxiv.org/abs/quant-ph/0301109"
},
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