The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential
We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and Pöschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that is independent of that parameter. Depending on an involved para...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/2769597 |
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| author | T. A. Ishkhanyan A. M. Ishkhanyan |
| author_facet | T. A. Ishkhanyan A. M. Ishkhanyan |
| author_sort | T. A. Ishkhanyan |
| collection | DOAJ |
| description | We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and Pöschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that is independent of that parameter. Depending on an involved parameter, the potential presents either a short-range singular well (which behaves as inverse square root at the origin and vanishes exponentially at infinity) or a smooth asymmetric step-barrier (with variable height and steepness). The general solution of the Schrödinger equation for this potential, which is a member of a general Heun family of potentials, is written through fundamental solutions each of which presents an irreducible linear combination of two Gauss ordinary hypergeometric functions. |
| format | Article |
| id | doaj-art-0d55c62190334616be12a92c9dd44a74 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-0d55c62190334616be12a92c9dd44a742025-02-03T01:02:45ZengWileyAdvances in High Energy Physics1687-73571687-73652018-01-01201810.1155/2018/27695972769597The Third Five-Parametric Hypergeometric Quantum-Mechanical PotentialT. A. Ishkhanyan0A. M. Ishkhanyan1Russian-Armenian University, Yerevan 0051, ArmeniaRussian-Armenian University, Yerevan 0051, ArmeniaWe introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and Pöschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that is independent of that parameter. Depending on an involved parameter, the potential presents either a short-range singular well (which behaves as inverse square root at the origin and vanishes exponentially at infinity) or a smooth asymmetric step-barrier (with variable height and steepness). The general solution of the Schrödinger equation for this potential, which is a member of a general Heun family of potentials, is written through fundamental solutions each of which presents an irreducible linear combination of two Gauss ordinary hypergeometric functions.http://dx.doi.org/10.1155/2018/2769597 |
| spellingShingle | T. A. Ishkhanyan A. M. Ishkhanyan The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential Advances in High Energy Physics |
| title | The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential |
| title_full | The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential |
| title_fullStr | The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential |
| title_full_unstemmed | The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential |
| title_short | The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential |
| title_sort | third five parametric hypergeometric quantum mechanical potential |
| url | http://dx.doi.org/10.1155/2018/2769597 |
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