Quantum-mechanical systems restricted by impenetrable barriers studied by a perturbation method

Abstract

A systematic perturbation method to calculate the explicit dependence of energy on the position of the repulsive barrier (or barriers) in one-dimensional non-degenerate systems is presented. The method is also capable of dealing with anisotropic shifts of the boundaries. Two simple applications illustrate the general principles (particle in a box and compression of the ground state of the hydrogen atom).