Logarithmic perturbation theory and its application to the Stark effect in a hydrogen atom

The technique considered earlier for calculating higher orders in perturbation theory (PT) in quantum mechanics is extended to excited states whose wave functions have nodes. Calculation of the Esub(k) coefficients of the PT series for the level energies reduces to recurrent relations which are convenient for numerical computation. As an example the Stark effect in the hydrogen atom is considered for states with n=1 or 2 and also for all states with n1=n2=0. The asymptotic value of Esub(k) for k → infinity which depends on the level width in weak fields in obtained. Summation of the divergent PT series makes it possible to determine the Stark shift and the level width in a strong electric field. The asymptotic value of the energy E(E) in extremely strong fields is found for a model which can be solved exactly (Stark effect for a one-dimensional delta- potential)