The Lambert-W step-potential – an exactly solvable confluent hypergeometric potential; Physics Letters A; Vol. 380, iss. 5-6
| Parent link: | Physics Letters A: Scientific Journal Vol. 380, iss. 5-6.— 2016.— [P. 640–644] |
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| Main Author: | |
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| Summary: | Title screen We present an asymmetric step–barrier potential for which the one-dimensional stationary Schrodinger equation is exactly solved in terms of the confluent hypergeometric functions. The potential is given in terms of the Lambert W-function, which is an implicitly elementary function also known as the product logarithm. We present the general solution of the problem and consider the quantum reflection at transmission of a particle above this potential barrier. Compared with the abrupt-step and hyperbolic tangent potentials, which are reproduced by the Lambert potential in certain parameter and/or variable variation regions, the reflection coefficient is smaller because of the lesser steepness of the potential on the particle incidence side. Presenting the derivation of the Lambert potential we show that this is a four-parametric sub-potential of a more general five-parametric one also solvable in terms of the confluent hypergeometric functions. The latter potential, however, is a conditionally integrable one. Finally, we show that there exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function. Режим доступа: по договору с организацией-держателем ресурса |
| Language: | English |
| Published: |
2016
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.physleta.2015.12.004 |
| Format: | Electronic Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=646318 |
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| 200 | 1 | |a The Lambert-W step-potential – an exactly solvable confluent hypergeometric potential |f A. Ishkhanyan | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a References: p. 644 (21 tit.) | ||
| 330 | |a We present an asymmetric step–barrier potential for which the one-dimensional stationary Schrodinger equation is exactly solved in terms of the confluent hypergeometric functions. The potential is given in terms of the Lambert W-function, which is an implicitly elementary function also known as the product logarithm. We present the general solution of the problem and consider the quantum reflection at transmission of a particle above this potential barrier. Compared with the abrupt-step and hyperbolic tangent potentials, which are reproduced by the Lambert potential in certain parameter and/or variable variation regions, the reflection coefficient is smaller because of the lesser steepness of the potential on the particle incidence side. Presenting the derivation of the Lambert potential we show that this is a four-parametric sub-potential of a more general five-parametric one also solvable in terms of the confluent hypergeometric functions. The latter potential, however, is a conditionally integrable one. Finally, we show that there exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Physics Letters A |o Scientific Journal | ||
| 463 | |t Vol. 380, iss. 5-6 |v [P. 640–644] |d 2016 | ||
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| 700 | 1 | |a Ishkhanyan |b A. |c physicist |c Junior Researcher of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1960- |g Artur |3 (RuTPU)RU\TPU\pers\36243 | |
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