On an inverse method in one dimension

Given a sequence of bound-state energies, the inverse Gel'fand-Levitan theory for the one-dimensional Schrödinger equation enables us to uniquely construct a symmetric reflectionless potential which supports those bound states. We test the reliability of this technique by applying it to some known symmetric potentials (confining and non-confining) in one dimension. We also study the systematics under which the method may be reliable.