The Spheroidal H Atom

Department of Chemistry Harvard University 12 Oxford Street Cambridge MA 02138, USA 

Beyond the interdimensional degeneracies, the three-dimensional nonrelativistic hydrogen atom is characterized by the extraordinary 

Although it is typically solved in spherical and parabolic coordinates, the hydrogenic Schrodinger equation is also separable in prolate spheroidal coordinates, with one focus at the nucleus and the other located along the Lenz vector at a distance R away. These coordinates are ordinarily used for two- center problems such as H. Previously, general features of the spheroidal hydrogen atom have been explored by Coulson and Robinson [6], who noted that the limits R — 0 and R — oo yield the spherical and parabolic solutions, respectively. Demkov [7] used the spheroidal eigenfunctions to construct 

For an electron at distances r and rt from two fixed Coulomb centers with charges Za and Zh a distance R apart, the wavefunction is separable in the form X(A)M(ju)e , with A = and /w =  

On substituting this into Equation (4) and simplifying with the aid of identities linking polynomials of different /, we obtsiin a three-term recursion relation for the coefficients  

---