Approximate bound state solutions of the Dunkl-Schrödinger equation for a hyperbolic double-well interaction
Axel Schulze‐Halberg
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.
Topics & Concepts
Bound statePhysicsState (computer science)Schrödinger equationMathematical physicsEquation of stateMathematicsMathematical analysisQuantum mechanicsAlgorithmQuantum Mechanics and Non-Hermitian PhysicsAdvanced Mathematical Physics ProblemsMathematical Analysis and Transform Methods