Approximate bound state solutions of the Dunkl-Schrödinger equation for a hyperbolic double-well interaction

2024/05/23 by Axel Schulze-Halberg, Axel Schulze‐Halberg · 3 citations
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods

paper · doi:10.1088/1402-4896/ad4fc8

Abstract

Abstract We construct approximate solutions to the stationary, one-dimensional Schrödinger equation for a hyperbolic double-well potential within the Dunkl formalism. Our approximation is applied to an inverse quadratic term contributed by the Dunkl formalism in the effective potential. The solutions we obtain are given in terms of confluent Heun functions. We establish parity of these solutions, discuss their elementary cases, and present an example of a system admitting bound states.

Citations

• Differential-difference operators associated to reflection groups

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• Exact Solutions of the Schrödinger-Dunkl Equation for a Free Particle in a Finite and Infinite Cylindrical Well

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