Solutions of the bi-confluent Heun equation in terms of the Hermite functions
| Parent link: | Annals of Physics Vol. 383.— 2017.— [P. 79-91] |
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| Main Author: | |
| Corporate Author: | |
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| Summary: | Title screen We construct an expansion of the solutions of the bi-confluent Heun equation in terms of the Hermite functions. The series is governed by a three-term recurrence relation between successive coefficients of the expansion. We examine the restrictions that are imposed on the involved parameters in order that the series terminates thus resulting in closed-form finite-sum solutions of the bi-confluent Heun equation. A physical application of the closed-form solutions is discussed. We present the five six-parametric potentials for which the general solution of the one-dimensional Schrцdinger equation is written in terms of the bi-confluent Heun functions and further identify a particular conditionally integrable potential for which the involved bi-confluent Heun function admits a four-term finite-sum expansion in terms of the Hermite functions. This is an infinite well defined on a half-axis. We present the explicit solution of the one-dimensional Schrцdinger equation for this potential and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and construct an accurate approximation for the bound-state energy levels. Режим доступа: по договору с организацией-держателем ресурса |
| Language: | English |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://doi.org/10.1016/j.aop.2017.04.015 |
| Format: | Electronic Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=656879 |
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| 200 | 1 | |a Solutions of the bi-confluent Heun equation in terms of the Hermite functions |f T. Ishkhanyan, A. Ishkhanyan | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: p. 91 (46 tit.)] | ||
| 330 | |a We construct an expansion of the solutions of the bi-confluent Heun equation in terms of the Hermite functions. The series is governed by a three-term recurrence relation between successive coefficients of the expansion. We examine the restrictions that are imposed on the involved parameters in order that the series terminates thus resulting in closed-form finite-sum solutions of the bi-confluent Heun equation. A physical application of the closed-form solutions is discussed. We present the five six-parametric potentials for which the general solution of the one-dimensional Schrцdinger equation is written in terms of the bi-confluent Heun functions and further identify a particular conditionally integrable potential for which the involved bi-confluent Heun function admits a four-term finite-sum expansion in terms of the Hermite functions. This is an infinite well defined on a half-axis. We present the explicit solution of the one-dimensional Schrцdinger equation for this potential and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and construct an accurate approximation for the bound-state energy levels. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Annals of Physics | ||
| 463 | |t Vol. 383 |v [P. 79-91] |d 2017 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a Bi-confluent Heun equation | |
| 610 | 1 | |a Series expansion | |
| 610 | 1 | |a ermite function | |
| 610 | 1 | |a уравнение Гойна | |
| 610 | 1 | |a уравнение Шредингера | |
| 700 | 1 | |a Ishkhanyan |b T. |g Tigran | |
| 701 | 1 | |a Ishkhanyan |b A. |c physicist |c Associate Scientist of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1960- |g Artur |3 (RuTPU)RU\TPU\pers\36243 | |
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