Residue-squaring iterative diagonalization method for perturbation problems

Abstract

We present a new method for the evaluation of the change in eigenvalues due to a perturbation of strength λ. It is a fast converging iterative method which, at thenth step, gives results accurate to order (2ⁿ⁺¹-1) in λ. Unlike the Rayleigh-Schrö dinger perturbation theory in quantum mechanics, which becomes prohibitively cumbersome when carried to higher orders, the present method involves a routine which remains stralghtforward at all stages.