Investigation of the Hylleraas Method for Determining the Potential-Energy Function from the Phase Shift

Abstract

The Hylleraas solution of the quantum mechanical inverse problem of scattering theory is discussed. A practical method for deducing the potential from the phase shift by this method and a variant upon it is described. A simple example (a model potential function) is used to illustrate the procedure. For this case, first‐order results are obtained analytically, higher‐order results by (extensive) numerical computations. The method converges properly if there are no bound states. However, for the model problem under investigation, the procedure converges to yield a phase‐equivalent potential when the potential well contains a bound state.