Hydrogen atom in a finite linear space (Q1979134)

In an earlier paper, a Galerkin-collocation-type techniques has been introduced which is based on a finite-dimensional matrix representation of a derivative obtained by Lagrange interpolation. In this paper, the technique is applied to calculate binding energies and eigenfunctions for the hydrogen atom. Three cases are considered: the Coulomb potential, the fine structure splitting, and the hydrogen atom in a uniform magnetic field. In the last case the problem is nonseparable in the coordinates and requires a modification of the method. Numerical results are presented.