Abstract The solution to the problem of a one-electron ion under the influence of various generalized central-field potentials is considered. Solutions are obtained using a finite expansion of the perturbation wave functions in terms of associated Laguerre polynomials. Higher orders of perturbation theory are obtained without having to perform integrations over the continuum states, and the solution can be written explicitly to any order. This perturbation procedure is applied to the three...

Abstract The non-relativistic energies have been determined for the singlet and triple S states (1¹S, 2¹S and 2³S) of the helium like two electron system. Calculations were based on a finite set of orbitals of the order 7. The set, which includes Laguerre polynomials, is expressed as a superposition of configurations built up from one-electron wave functions or orbitals and approximates the exact wave function. Application of the variational principle leads to a system of linear equations....