A new exactly integrable hypergeometric potential for the Schrödinger equation

T. A. Ishkhanyan; V. A. Manukyan; A. H. Harutyunyan; A. M. Ishkhanyan

doi:10.1063/1.5022086

paper

A new exactly integrable hypergeometric potential for the Schrödinger equation

arXiv:1803.05363 · doi:10.1063/1.5022086

Abstract

We introduce a new exactly integrable potential for the Schrödinger equation for which the solution of the problem may be expressed in terms of the Gauss hypergeometric functions. This is a potential step with variable height and steepness. We present the general solution of the problem, discuss the transmission of a quantum particle above the barrier, and derive explicit expressions for the reflection and transmission coefficients.