LARGE-ORDER PERTURBATION-THEORY WITHOUT A WAVE-FUNCTION FOR THE LOSURDO-STARK EFFECT IN HYDROGENIC ATOMS

I obtain exact large-order perturbation corrections to the energy shifts of the LoSurdo-Stark effect in hydrogenic atoms for both non-degenerate and degenerate states. The method consists of applying perturbation theory to a recurrence relation among properly selected moments of the eigenfunction which do not explicitly appear in the calculation. The resulting recurrence relation for the perturbation corrections is suitable for computer algebra calculation of perturbation corrections to the energy. The method is most useful to treat both separable and non-separable problems in any convenient coordinate system. Here I use spherical polar coordinates and calculate the shifts of the first two hydrogenic energy levels as illustrative examples.