The third exactly solvable hypergeometric quantum-mechanical potential
Institute for Physical Research, NAS of Armenia - 0203, Ashtarak, Armenia and Institute of Physics and Technology, National Research Tomsk Polytechnic University - 634050, Tomsk, Russia
Received: 8 July 2016
Accepted: 30 July 2016
We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the Pöschl-Teller potentials, which is proportional to an energy-independent parameter and has a shape that is independent of this parameter. The general solution of the Schrödinger equation for this potential is written through fundamental solutions each of which presents an irreducible combination of two Gauss hypergeometric functions. The potential is an asymmetric step-barrier with variable height and steepness. Discussing the transmission above such a barrier, we derive a compact formula for the reflection coefficient.
PACS: 03.65.Ge – Solutions of wave equations: bound states / 02.30.Ik – Integrable systems / 02.30.Gp – Special functions
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