A new exactly integrable hypergeometric potential for the Schr\"odinger equation
T.A. Ishkhanyan, V.A. Manukyan, A.H. Harutyunyan, and A.M. Ishkhanyan
TL;DR
This paper introduces a novel exactly solvable hypergeometric potential in the Schrödinger equation, allowing explicit solutions and analysis of quantum particle transmission over a variable barrier.
Contribution
The paper presents a new exactly integrable potential expressed via hypergeometric functions, expanding solvable models in quantum mechanics.
Findings
Explicit solutions for the Schrödinger equation with the new potential
Derived formulas for reflection and transmission coefficients
Analysis of quantum particle transmission over variable barriers
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.
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