A bound-state perturbation expansion with superior convergence properties

A perturbation method is presented which, while using the same Born elements as the Rayleigh–Schrödinger (RS) theory, does not use an expansion in powers of the perturbation parameter. Its use will give a convergent sequence of approximations in problems where the RS series may be asymptotic or divergent. By using RS basis set the physical interpretation of the RS theory is retained, unlike some alternate methods. Computationally, in the first few orders, it is only slightly more difficult than the RS method. Some simple examples are presented which illustrates the convergence properties in relation to the RS series.