Logarithmic perturbation expansion for the Dirac equation in one dimension: Application to the polarizability calculation

The method of logarithmic perturbation expansion which was developed by Aharonov and Au for the Schrödinger equation is extended to the Dirac equation in one dimension. The method enables us to calculate the perturbed energy and wave function of a bound state without involving summation over intermediate states. The method is illustrated by applying it to the calculation of the polarizability of a bound system which is subject to a linear perturbation. The notion of anti-polarization, which is peculiar to relativistic bound systems, is discussed.