Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity

Abstract

We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential, which belongs to a general Heun family, is a short-range one that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. We derive the exact spectrum equation for the energy and discuss the bound states supported by the potential.

Original language	English
Article number	83
Journal	European Physical Journal Plus
Volume	133
Issue number	3
DOIs	https://doi.org/10.1140/epjp/i2018-11912-5
Publication status	Published - 1 Mar 2018

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1140/epjp/i2018-11912-5

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title = "Exact solution of the Schr{\"o}dinger equation for a short-range exponential potential with inverse square root singularity",

abstract = "We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schr{\"o}dinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential, which belongs to a general Heun family, is a short-range one that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. We derive the exact spectrum equation for the energy and discuss the bound states supported by the potential.",

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AB - We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential, which belongs to a general Heun family, is a short-range one that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. We derive the exact spectrum equation for the energy and discuss the bound states supported by the potential.

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