A rigorous foundation of an easy-to-apply approximation method for bound state problems

Recently the application of a non-expensive scattering theory method to bound state problems has been proposed on the grounds of intuitive arguments. Subsequent realistic calculations have manifested advantageous features of the method especially in problems in which the asymptotic behaviour of the wave function is important. Here it is rigorously proven that the method is convergent, and mathematically correct procedures are described that speed up convergence and make the approximate energies approach the exact value from one side only. The general considerations are visualized by numerical results of a model problem.