Bound states in a hyperbolic asymmetric double-well

TL;DR

This paper introduces a new class of hyperbolic asymmetric double-well potentials with bound states described by confluent Heun functions, providing an analytic method to determine energy levels and bound state conditions.

Contribution

It presents a novel hyperbolic asymmetric double-well model with bound states expressed via confluent Heun functions and develops an analytic approach for energy eigenvalues.

Findings

Bound states are described by confluent Heun functions.

An analytic procedure for energy eigenvalues is established.

Criteria for bound state support are discussed.

Abstract

We report a new class of hyperbolic asymmetric double-well whose bound state wavefunctions can be expressed in terms of confluent Heun functions. An analytic procedure is used to obtain the energy eigenvalues and the criterion for the potential to support bound states is discussed.