Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r

For pt.I, see ibid., vol.20, no.8, p.2043-75 (1987). Several coordinate systems for solving the few-electron Schrodinger equation are presented. Formal solutions corresponding to each coordinate system are given in terms of the Fock expansion and their interrelationships and general structure are examined. Attention is focused on the solutions obtained using spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction is obtained up to second order in the hyperradius r=(r² ₁+r(sup)2 ₂)¹2/, and the special case of ¹S states is then reduced to a closed form using classical techniques. The insight gained from this reduction suggests methods for solving the wavefunction to all orders. The results hint at the existence of closed form wavefunctions for few-body systems.