Wave Functions for the Hydrogen Atom in Spheroidal Coordinates II: Interaction with a Point Charge and with a Dipole

Abstract

The interactions of a point charge and of a point dipole with a hydrogen atom are investigated. Interaction energies, dipole and quadrupole moments are calculated using exact perturbation theory. Spheroidal coordinates are necessary to solve the differential equations which arise, and wave functions for the atom in these coordinates are seen to be the correct zero-order ones to use. The exact form of the perturbing potential is employed, giving results with both polynomial and exponentially decreasing terms. These are compared with the simpler but less accurate results obtained when the expanded form of the perturbation is used.