Potentials of the Heun class

D. Batic; R. Williams; M. Nowakowski

doi:10.1088/1751-8113/46/24/245204

Potentials of the Heun class

D. Batic, R. Williams, M. Nowakowski

Mathematics

Research output: Contribution to journal › Review article › peer-review

27 Scopus citations

Abstract

We review different methods of generating potentials such that the one-dimensional Schrödinger equation (ODSE) can be transformed into the hypergeometric equation. We compare our results with previous studies, and complement the subject with new findings. Our main result is to derive new classes of potentials such that the ODSE can be transformed into the Heun equation and its confluent cases. The generalized Heun equation is also considered.

Original language	British English
Article number	245204
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	46
Issue number	24
DOIs	https://doi.org/10.1088/1751-8113/46/24/245204
State	Published - 21 Jun 2013

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10.1088/1751-8113/46/24/245204

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title = "Potentials of the Heun class",

abstract = "We review different methods of generating potentials such that the one-dimensional Schr{\"o}dinger equation (ODSE) can be transformed into the hypergeometric equation. We compare our results with previous studies, and complement the subject with new findings. Our main result is to derive new classes of potentials such that the ODSE can be transformed into the Heun equation and its confluent cases. The generalized Heun equation is also considered.",

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T1 - Potentials of the Heun class

AU - Batic, D.

AU - Williams, R.

AU - Nowakowski, M.

PY - 2013/6/21

Y1 - 2013/6/21

N2 - We review different methods of generating potentials such that the one-dimensional Schrödinger equation (ODSE) can be transformed into the hypergeometric equation. We compare our results with previous studies, and complement the subject with new findings. Our main result is to derive new classes of potentials such that the ODSE can be transformed into the Heun equation and its confluent cases. The generalized Heun equation is also considered.

AB - We review different methods of generating potentials such that the one-dimensional Schrödinger equation (ODSE) can be transformed into the hypergeometric equation. We compare our results with previous studies, and complement the subject with new findings. Our main result is to derive new classes of potentials such that the ODSE can be transformed into the Heun equation and its confluent cases. The generalized Heun equation is also considered.

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DO - 10.1088/1751-8113/46/24/245204

M3 - Review article

AN - SCOPUS:84878789608

SN - 1751-8113

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 24

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Potentials of the Heun class

Abstract

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