Spherical-Coordinate Analysis of Ground-State Energy Eigenfunctions for an Electron in the Field of a Finite Dipole

Ground-state energy eigenfunctions for an electron in the field of a stationary, finite dipole are obtained in spherical polar coordinates. The analysis is made in two systems, one with origin at the positive dipole charge and the other with origin at the dipole center. Results show the number of partial waves needed as a function of dipole moment $D$, and the structure of the radial functions throughout space. No regular nodal pattern in the radial functions for different angular momentum partial waves was noted. The functions expressed in spherical coordinates are available numerically for use in other calculations.