A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions; Modern Physics Letters A; Vol. 31, iss. 33
| Parent link: | Modern Physics Letters A: Scientific Journal.— , 1986- Vol. 31, iss. 33.— 2016.— [1650177, 13 р.] |
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| Riassunto: | Title screen We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrödinger equation is written through the first derivative of a double-confluent Heun function. One of these potentials is a singular potential that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. The exact solution of the Schrödinger equation for this potential is given through fundamental solutions each of which presents an irreducible linear combination of two confluent hypergeometric functions. Since the potential is effectively a short-range one it supports only a finite number of bound states. |
| Lingua: | inglese |
| Pubblicazione: |
2016
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| Accesso online: | http://dx.doi.org/10.1142/S0217732316501777 |
| Natura: | MixedMaterials Elettronico Capitolo di libro |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=653886 |
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| 200 | 1 | |a A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions |f A. Ishkhanyan | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 47 tit.] | ||
| 330 | |a We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrödinger equation is written through the first derivative of a double-confluent Heun function. One of these potentials is a singular potential that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. The exact solution of the Schrödinger equation for this potential is given through fundamental solutions each of which presents an irreducible linear combination of two confluent hypergeometric functions. Since the potential is effectively a short-range one it supports only a finite number of bound states. | ||
| 461 | |t Modern Physics Letters A |o Scientific Journal |d 1986- | ||
| 463 | |t Vol. 31, iss. 33 |v [1650177, 13 р.] |d 2016 | ||
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| 610 | 1 | |a гипергеометрические функции | |
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| 610 | 1 | |a бесконечность | |
| 700 | 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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