Ground-State Energy Eigenvalues and Eigenfunctions for an Electron in an Electric-Dipole Field

Ground-state energy eigenvalues and eigenfunctions are obtained by a variational method for an electron in the field of a finite, stationary, permanent electric dipole. The dipole moments studied cover the range from the minimum value required for binding (Dₘᵢₙ=0.6393 ea₀) to D=400 ea₀, where the system is equivalent to the hydrogen atom perturbed slightly by a distant stationary negative charge. The eigenvalues obtained agree with those reported by Wallis, Herman, and Milnes, who determined them by another method in the range D=0.84ea₀ to 30ea₀. The normalized eigenfunctions display the manner in which the electronic charge density changes from that of the hydrogen atom at very large D to a flat distribution approaching that which is characteristic of a zero-energy continuum state as the minimum moment is approached from above. Optimized variational wave functions for different values of D are presented for use in other calculations. Contour maps and profiles of electronic charge density are shown for a number of values of D. Mean values of the powers -1, 1, and 2 of the distances of the electron from the dipole charges are also calculated.