On a solution of the Schrödinger equation with a hyperbolic double-well potential

Abstract

We report a solution of the one-dimensional Schrödinger equation with a hyperbolic double-well confining potential via a transformation to the so-called confluent Heun equation. We discuss the requirements on the parameters of the system in which a reduction to confluent Heun polynomials is possible, representing the wavefunctions of bound states.