A conditionally exactly solvable generalization of the inverse square root potential; Physics Letters A; Vol. 380, iss. 45
| Parent link: | Physics Letters A Vol. 380, iss. 45.— 2016.— [P. 3786–3790] |
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| Summary: | Title screen We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. 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.2016.09.035 |
| Format: | Electronic Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=654336 |
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| 200 | 1 | |a A conditionally exactly solvable generalization of the inverse square root potential |f A. Ishkhanyan | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: p. 3789-3790 (30 tit.)] | ||
| 330 | |a We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Physics Letters A | ||
| 463 | |t Vol. 380, iss. 45 |v [P. 3786–3790] |d 2016 | ||
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| 610 | 1 | |a гипергеометрические функции | |
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| 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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