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| 005 | 20231030041448.0 | ||
| 035 | _a(RuTPU)RU\TPU\network\23359 | ||
| 090 | _a656879 | ||
| 100 | _a20171218a2017 k y0engy50 ba | ||
| 101 | 0 | _aeng | |
| 102 | _aNL | ||
| 135 | _adrcn ---uucaa | ||
| 181 | 0 | _ai | |
| 182 | 0 | _ab | |
| 200 | 1 |
_aSolutions of the bi-confluent Heun equation in terms of the Hermite functions _fT. Ishkhanyan, A. Ishkhanyan |
|
| 203 |
_aText _celectronic |
||
| 300 | _aTitle screen | ||
| 320 | _a[References: p. 91 (46 tit.)] | ||
| 330 | _aWe 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 | _aРежим доступа: по договору с организацией-держателем ресурса | ||
| 461 | _tAnnals of Physics | ||
| 463 |
_tVol. 383 _v[P. 79-91] _d2017 |
||
| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 610 | 1 | _aBi-confluent Heun equation | |
| 610 | 1 | _aSeries expansion | |
| 610 | 1 | _aermite function | |
| 610 | 1 | _aуравнение Гойна | |
| 610 | 1 | _aуравнение Шредингера | |
| 700 | 1 |
_aIshkhanyan _bT. _gTigran |
|
| 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 |
|
| 712 | 0 | 2 |
_aНациональный исследовательский Томский политехнический университет (ТПУ) _bФизико-технический институт (ФТИ) _bКафедра общей физики (ОФ) _h136 _2stltpush _3(RuTPU)RU\TPU\col\18734 |
| 801 | 2 |
_aRU _b63413507 _c20171225 _gRCR |
|
| 856 | 4 | _uhttps://doi.org/10.1016/j.aop.2017.04.015 | |
| 942 | _cCF | ||