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 A survey of the relative efficiency of various approximate methods for solving the non-relativistic Schroedinger Equation [sic] is made. In particular, a comparison is made of the results obtained for the problem of a simple harmonic oscillator perturbed by λx∝, (∝ =3,4 ) while using the Rayleigh-Ritz variational principle, Linear Variation of Functions, and the Reyleigh-Schroedinger [sic]...

Abstract In Part I, a large parameter asymptotic expansion of a perturbed simple harmonic oscillator is presented. Perturbations of the form λx∝ are studied were λ is the coupling constant. The method is demonstrated by a general derviation of the wavefunctions to third order for any ∝ and quantum number n. Additonal expressions are presented for the ground states to tenth order in the energy. It is also shown that the "matching condition" for the basic and...