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arXiv · 1803.05363

A new exactly integrable hypergeometric potential for the Schrödinger equation

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

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T. A. Ishkhanyan, V. A. Manukyan, A. H. Harutyunyan, A. M. Ishkhanyan. 2018-03-12. A new exactly integrable hypergeometric potential for the Schrödinger equation. https://doi.org/10.1063/1.5022086

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