dorsal/arxiv
View SchemaSecond Order Darboux Displacements
| Authors | B F Samsonov, M L Glasser, J Negro, L M Nieto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307146 |
| URL | https://arxiv.org/abs/quant-ph/0307146 |
| DOI | 10.1088/0305-4470/36/39/306 |
| Journal | J. Phys. A: Math. Gen. 36 (2003) 10053--10069 |
Abstract
The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived.
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"abstract": "The potentials for a one dimensional Schroedinger equation that are displaced\nalong the x axis under second order Darboux transformations, called 2-SUSY\ninvariant, are characterized in terms of a differential-difference equation.\nThe solutions of the Schroedinger equation with such potentials are given\nanalytically for any value of the energy. The method is illustrated by a\ntwo-soliton potential. It is proven that a particular case of the periodic\nLame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the\ncorresponding Schroedinger equation equation are found for any value of the\nenergy. A simple analytic expression for a family of two-gap potentials is\nderived.",
"arxiv_id": "quant-ph/0307146",
"authors": [
"B F Samsonov",
"M L Glasser",
"J Negro",
"L M Nieto"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/36/39/306",
"journal_ref": "J. Phys. A: Math. Gen. 36 (2003) 10053--10069",
"title": "Second Order Darboux Displacements",
"url": "https://arxiv.org/abs/quant-ph/0307146"
},
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