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 (${D}_{min}=0.6393 e{a}_{0}$) to $D=400 e{a}_{0}$, 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 $D=0.84e{a}_{0} \mathrm{to} 30e{a}_{0}$. 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.

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