On the perturbation theory of small disturbances

Abstract

As a preliminary to a wide range of applications, conventional perturbation theory is re-examined and a number of useful properties emphasized. It is shown in particular that the total, kinetic and potential energies can be obtained to the (2 s + 1)th order from a knowledge of only the s th-order wave function and that similar though less powerful theorems hold for other diagonal matrix elements. A combination of variational and perturbation techniques is suggested as the best method of calculating small disturbances of a stationary system.