Transition from Discrete to Continuous Spectra

Abstract

The stationary states of a system bound in a spherical box and additionally subjected to a perturbation of finite range are studied in the limit as the box radius becomes infinite. The transition from formal discrete-spectrum theory to formal scattering theory is carried out explicitly by two different methods. It is shown quite generally (i.e., even when the total Hamiltonian is not separable) that the level shift produced by the perturbation is proportional to the corresponding scattering phase shift.