| 000 | 03062nlm1a2200433 4500 | ||
|---|---|---|---|
| 001 | 664730 | ||
| 005 | 20231030041939.0 | ||
| 035 | _a(RuTPU)RU\TPU\network\35914 | ||
| 035 | _aRU\TPU\network\28873 | ||
| 090 | _a664730 | ||
| 100 | _a20210514a2018 k y0engy50 ba | ||
| 101 | 0 | _aeng | |
| 135 | _adrcn ---uucaa | ||
| 181 | 0 | _ai | |
| 182 | 0 | _ab | |
| 200 | 1 |
_aA conditionally integrable bi-confluent Heun potential involving inverse square root and centrifugal barrier terms _fT. A. Ishkhanyan, V. P. Kraynov, A. Ishkhanyan |
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| 203 |
_aText _celectronic |
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| 300 | _aTitle screen | ||
| 330 | _aWe present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrodinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term x-1/2 with arbitrary strength and a repulsive centrifugal barrier core x-2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrodinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels. | ||
| 333 | _aРежим доступа: по договору с организацией-держателем ресурса | ||
| 461 | _tZeitschrift fur Naturforschung - Section A Journal of Physical Sciences | ||
| 463 |
_tVol. 73, iss. 5 _v[P. 407-414] _d2018 |
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| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 610 | 1 | _aBi-confluent Heun equation | |
| 610 | 1 | _aHermite function | |
| 610 | 1 | _aintegrable potentials | |
| 610 | 1 | _astationary Schrödinger equation | |
| 610 | 1 | _aquantum physics | |
| 610 | 1 | _aquantum physics | |
| 610 | 1 | _aэнергетические спектры | |
| 610 | 1 | _aуравнение Гойна | |
| 700 | 1 |
_aenergy spectrum _bT. A. _gTigran Arturovich |
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| 701 | 1 |
_aKraynov _bV. P. _gVladimir Pavlovich |
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| 701 | 1 |
_aIshkhanyan _bA. _cphysicist _cAssociate Scientist of Tomsk Polytechnic University, Doctor of physical and mathematical sciences _f1960- _gArtur _2stltpush _3(RuTPU)RU\TPU\pers\36243 |
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| 712 | 0 | 2 |
_aНациональный исследовательский Томский политехнический университет _bИнженерная школа ядерных технологий _bОтделение экспериментальной физики _h7865 _2stltpush _3(RuTPU)RU\TPU\col\23549 |
| 801 | 2 |
_aRU _b63413507 _c20210514 _gRCR |
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| 856 | 4 | _uhttps://doi.org/doi:10.1515/zna-2017-0314 | |
| 942 | _cCF | ||