Schrödinger potentials solvable in terms of the confluent Heun functions

Schrödinger potentials solvable in terms of the confluent Heun functions

Bibliographic Details
Parent link:Theoretical and Mathematical Physics
Vol. 188, iss. 1.— 2016.— [P. 980-993]
Main Author: Ishkhanyan A. Artur
Corporate Author: Национальный исследовательский Томский политехнический университет Физико-технический институт Кафедра общей физики
Summary:Title screen
We show that if the potential is proportional to an energy-independent continuous parameter, then there exist 15 choices for the coordinate transformation that provide energy-independent potentials whose shape is independent of that parameter and for which the one-dimensional stationary Schrцdinger equation is solvable in terms of the confluent Heun functions. All these potentials are also energy-independent and are determined by seven parameters. Because the confluent Heun equation is symmetric under transposition of its regular singularities, only nine of these potentials are independent. Five of the independent potentials are different generalizations of either a hypergeometric or a confluent hypergeometric classical potential, one potential as special cases includes potentials of two hypergeometric types (the Morse confluent hypergeometric and the Eckart hypergeometric potentials), and the remaining three potentials include five-parameter conditionally integrable confluent hypergeometric potentials. Not one of the confluent Heun potentials, generally speaking, can be transformed into any other by a parameter choice.
Режим доступа: по договору с организацией-держателем ресурса
Language:English
Published: 2016
Subjects:
электронный ресурс
труды учёных ТПУ
Online Access:http://dx.doi.org/10.1134/S0040577916070023
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=650553

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