International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 2, Pages 351-368
doi:10.1155/S0161171280000245

Closed form bound-state perturbation theory

Abstract

The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.