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arXiv · 1801.07247

The third five-parametric hypergeometric quantum-mechanical potential

T. A. Ishkhanyan·A. M. Ishkhanyan
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Abstract

We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and Pöschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that is independent of that parameter. Depending on an involved parameter, the potential presents either a short-range singular well (which behaves as inverse square root at the origin and vanishes exponentially at infinity) or a smooth asymmetric step-barrier (with variable height and steepness). The general solution of the Schrödinger equation for this potential, which is a member of a general Heun family of potentials, is written through fundamental solutions each of which presents an irreducible linear combination of two Gauss ordinary hypergeometric functions.

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T. A. Ishkhanyan, A. M. Ishkhanyan. 2018-01-19. The third five-parametric hypergeometric quantum-mechanical potential. https://doi.org/10.1155/2018%2F2769597

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