Appraisal of the FOPIM Fast-Converging Perturbation Method

Abstract
The practicality of the first‐order perturbation‐iteration method (FOPIM) is appraised. After the first iteration, the expectation value of the energy is given by a nonanalytic function of the perturbation parameter λ. The asymptotic expansion of this function gives the energy accurately up to O8). The convergence of the asymptotic expansions is discussed. Two examples are considered: a perturbed ground‐state hydrogen atom, and a perturbed ground‐state linear harmonic oscillator.