A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions

A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions

Bibliographic Details
Parent link:Modern Physics Letters A: Scientific Journal.— , 1986-
Vol. 31, iss. 33.— 2016.— [1650177, 13 р.]
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 introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrödinger equation is written through the first derivative of a double-confluent Heun function. One of these potentials is a singular potential that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. The exact solution of the Schrödinger equation for this potential is given through fundamental solutions each of which presents an irreducible linear combination of two confluent hypergeometric functions. Since the potential is effectively a short-range one it supports only a finite number of bound states.
Language:English
Published: 2016
Subjects:
электронный ресурс
труды учёных ТПУ
уравнение Шредингера
гипергеометрические функции
квадратные корни
бесконечность
Online Access:http://dx.doi.org/10.1142/S0217732316501777
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=653886

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