Quantum inversion with elastic phase shifts to discrete different energies

Abstract

We consider the inverse quantum scattering problem with phase shifts of different discrete energies belonging to a real energy-independent radial potential for elastic scattering. The solution of this problem is essential for atomic and nuclear physics. The two procedures investigated are based on the modified Newton–Sabatier method. The first procedure leads to angular-momentum dependent potentials with poles. The second one carries out an inversion at a fixed energy by varying the phase shifts of the other energies and leads finally to the correct energy-independent potential.