On the calculation of bound-state energies supported by hyperbolic double well potentials

Abstract

We obtain eigenvalues and eigenfunctions of the Schrödinger equation with a hyperbolic double-well potential. We consider exact polynomial solutions for some particular values of the potential-strength parameter and also numerical energies for arbitrary values of this model parameter. We test the numerical method by means of a suitable exact asymptotic expression for the eigenvalues and also calculate critical values of the strength parameter that are related to the number of bound states supported by the potential.