An example of double confluent Heun equation: Schroedinger equation with supersingular plus Coulomb potential

Abstract

A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a repulsive supersingular term, Ar(-4), plus an attractive Coulombian one, -Zr(-1). The existence of exact algebraic solutions for certain values of A is discussed.