The Riemann solution and the inverse quantum mechanical problem

Abstract

Systematic use is made of the Riemann function to find the conditions for the existence of the kernel of the inverse problem at fixed value of the angular momentum. When the reference potential is the centrifugal one, only an l-dependent condition on the potential must be required in the Marchenko case; in the Gel’fand–Levitan case, the condition is l-independent. When the Coulomb potential is included in the reference potential, an exponential decrease of the potential is needed in both instances.