dorsal/arxiv
View SchemaNew Solvable and Quasi Exactly Solvable Periodic Potentials
| Authors | Avinash Khare, Uday Sukhatme |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906044 |
| URL | https://arxiv.org/abs/quant-ph/9906044 |
| DOI | 10.1063/1.533040 |
| Journal | J.Math.Phys. 40 (1999) 5473-5494 |
Abstract
Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lame potentials ma(a+1)sn^2(x,m) are computed for integer values a=1,2,3,.... For all cases (except a=1), we show that the partner potential is distinctly different from the original Lame potential, even though they both have the same energy band structure. We also derive and discuss the energy band edges of the associated Lame potentials pm sn^2(x,m)+qm cn^2(x,m)/ dn^2(x,m), which constitute a much richer class of periodic problems. Computation of their supersymmetric partners yields many additional new solvable and quasi exactly solvable periodic potentials.
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"abstract": "Using the formalism of supersymmetric quantum mechanics, we obtain a large\nnumber of new analytically solvable one-dimensional periodic potentials and\nstudy their properties. More specifically, the supersymmetric partners of the\nLame potentials ma(a+1)sn^2(x,m) are computed for integer values a=1,2,3,....\nFor all cases (except a=1), we show that the partner potential is distinctly\ndifferent from the original Lame potential, even though they both have the same\nenergy band structure. We also derive and discuss the energy band edges of the\nassociated Lame potentials pm sn^2(x,m)+qm cn^2(x,m)/ dn^2(x,m), which\nconstitute a much richer class of periodic problems. Computation of their\nsupersymmetric partners yields many additional new solvable and quasi exactly\nsolvable periodic potentials.",
"arxiv_id": "quant-ph/9906044",
"authors": [
"Avinash Khare",
"Uday Sukhatme"
],
"categories": [
"quant-ph",
"cond-mat",
"hep-th"
],
"doi": "10.1063/1.533040",
"journal_ref": "J.Math.Phys. 40 (1999) 5473-5494",
"title": "New Solvable and Quasi Exactly Solvable Periodic Potentials",
"url": "https://arxiv.org/abs/quant-ph/9906044"
},
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