A conditionally exactly solvable generalization of the inverse square root potential

A conditionally exactly solvable generalization of the inverse square root potential

Bibliographic Details
Parent link:Physics Letters A
Vol. 380, iss. 45.— 2016.— [P. 3786–3790]
Main Author: Ishkhanyan A. Artur
Corporate Author: Национальный исследовательский Томский политехнический университет (ТПУ) Физико-технический институт (ФТИ) Кафедра общей физики (ОФ)
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
Published: 2016
Subjects:
труды учёных ТПУ
электронный ресурс
стационарные уравнения
уравнение Шредингера
линейные комбинации
гипергеометрические функции
энергетические спектры
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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