A change of variable for the perturbation parameter in rayleigh–Schrödinger perturbation theory

The Feenberg–Goldhammer change of scale, whereby the H 0 in perturbation theory is replaced by (1/μ) H 0 with μ a scaling parameter, is shown to be equivalent to a change of variable for the perturbation parameter. A more general change of variable is shown to lead to a perturbation series with perturbation energies E 3 , …, E 2n+1 equal to zero. The resulting energy through (2 n + 1)th order has the same form as that found from the Brillouin–Wigner series by different methods.