Logarithmic perturbation theory: A reappraisal*

We present logarithmic perturbation theory in its simplest form that rests only on matching of certain polynomial coefficients at each order. It thus avoids any integration step in the course of calculations of energy correction terms at various orders. The scheme applies to excited states as well. Corrections to nodal point shifts are also obtained without quadratures. A few existing variants of the theory are compared and certain anomalies rectified. Merits and demerits of the approach are pointed out. We also outline a direct route to obtain perturbation series for properties through this route. This renders tedious computations of wave function correction terms at each order, obeying the corresponding normalization requirement, unnecessary, thus achieving further simplification. Pilot calculations on several model systems reveal the worth of the endeavor.