Year: 2016
Type: article
Abstract: 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.
Source: Europhysics Letters (EPL)
Author: Artur Ishkhanyan
Institutions: Tomsk Polytechnic University, Institute for Physical Research
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G2591136160, G4802465088
OpenAlex ID: W2273920331