Soft-core Coulomb potentials and Heun's differential equation

Abstract

Schroedinger's equation with the attractive potential V(r) = -Z/(r^q+ b^q)^(1/q), Z > 0, b > 0, q >= 1, is shown, for general values of the parameters Z and b, to be reducible to the confluent Heun equation in the case q=1, and to the generalized Heun equation in case q=2. In a formulation with correct asymptotics, the eigenstates are specified a priori up to an unknown factor. In certain special cases this factor becomes a polynomial. The Asymptotic Iteration Method is used either to find the polynomial factor and the associated eigenvalue explicitly, or to construct accurate approximations for them. Detail solutions for both cases are provided.

16 pages, no figures

References in corpus (5)

• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
• Asymptotic Iteration method for singular potentials
• Energies and wave functions for a soft-core Coulomb potential
• Solutions for certain classes of Riccati differential equation

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