English

A new exactly integrable hypergeometric potential for the Schr\"odinger equation

Quantum Physics 2018-03-15 v1

Abstract

We introduce a new exactly integrable potential for the Schr\"odinger 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.

Keywords

Cite

@article{arxiv.1803.05363,
  title  = {A new exactly integrable hypergeometric potential for the Schr\"odinger equation},
  author = {T. A. Ishkhanyan and V. A. Manukyan and A. H. Harutyunyan and A. M. Ishkhanyan},
  journal= {arXiv preprint arXiv:1803.05363},
  year   = {2018}
}
R2 v1 2026-06-23T00:53:08.312Z