Excited states in logarithmic perturbation theory

It is generally assumed that in the logarithmic perturbation method the magnitudes of the corrections to the logarithm of the unperturbed wave function become infinite at the points at which the wave function has zeros. Therefore, for excited states special devices, which greatly complicate the calculation, have been proposed. It is shown in this paper that in many cases the excited states can be calculated without these complications by using the formulas for the ground state; the corrections in this case remain finite at the zero points. A general criterion for the existence of such cases is given. The need for special devices is also eliminated for states for which the current is nonzero. It is shown that the logarithmic perturbation method proposed by the authors in an earlier study (1971) for excited states simplifies appreciably in problems with a local perturbing potential.