The Heun-Schrodinger radial equation for DH-atoms

摘要

This article deals with the connection between Schrodinger's multidimensional equation for DH-atoms (D >= 1) and the confluent Heun equation with two auxiliary parameters v and tau, where /1-v/ = o(1) and tau epsilon Q(+), which influence the spectrum of eigenvalues, the Coulomb potential and the radial function. The case tau = v = 1 and D = 3 corresponds to the "standard" form of Schrodinger's equation for a 3H-atom. With the help of parameter v, e.g., some "quantum corrections" may be considered. The cases 0 < tau < 1 and tau > 1, but (a) over cap = (n - l - 1)tau >= 0 is an integer, change the "geometry" of the electron cloud in the atom, i.e. the so-called "exotic" 3H-like atoms arise, where Kummer's function F-1(1) (-(a) over cap; c; z) has (a) over cap zeros and the discrete spectrum depends only on Z/(vn) but not on l and tau. Diagrams of the radial functions (P) over cap (nl) (r; tau, v) as n <= 3 are given.