THE HEUN–SCHRÖDINGER RADIAL EQUATION WITH TWO AUXILIARY PARAMETERS FOR H-LIKE ATOMS

Abstract

This article deals with the connection between the confluent Heun equation (with two singularities 0 and ∞) and Schrödinger's equation for H-like atoms with two "auxiliary" parameters μ and ν which "influence" the spectrum of eigenvalues, the Coulomb potential and also the radial function. The case of μ = ν = 1 corresponds to the "standard" form of Schrödinger's equation. In terms of the parameter ν, for example, "relativistic corrections" of the type: Dirac's formula of the fine structure, the nuclear motion, etc., may be considered.