A conditionally integrable bi-confluent Heun potential involving inverse square root and centrifugal barrier terms; Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences; Vol. 73, iss. 5

A conditionally integrable bi-confluent Heun potential involving inverse square root and centrifugal barrier terms; Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences; Vol. 73, iss. 5

Библиографические подробности
Источник:Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
Vol. 73, iss. 5.— 2018.— [P. 407-414]
Главный автор: energy spectrum T. A. Tigran Arturovich
Автор-организация: Национальный исследовательский Томский политехнический университет Инженерная школа ядерных технологий Отделение экспериментальной физики
Другие авторы: Kraynov V. P. Vladimir Pavlovich, Ishkhanyan A. Artur
Примечания:Title screen
We 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.
Режим доступа: по договору с организацией-держателем ресурса
Язык:английский
Опубликовано: 2018
Предметы:
электронный ресурс
труды учёных ТПУ
Bi-confluent Heun equation
Hermite function
integrable potentials
stationary Schrödinger equation
quantum physics
энергетические спектры
уравнение Гойна
Online-ссылка:https://doi.org/doi:10.1515/zna-2017-0314
Формат: Электронный ресурс Статья
Запись в KOHA:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=664730

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