Quasi-Exactly Solvable Singular Fractional Power Potentials Emerging from the Triconfluent Heun Equation

Abstract

We consider a triconfluent Heun equation (TCHE) possessing infinitely many Liouvillian solutions and transform it into a radial Schrödinger equation for a general power law potential. From the latter we extract three special cases, namely different singular fractional power potentials (SFPP) for which the transformed Liouvillian solutions of the original TCHE represent Schrödinger bound states. Hence we obtain an infinite set of exact Schrödinger bound state solutions and corresponding energies for each of the three SFPP.