The Discrete Spectrum and the Continuum

One-body Hamiltonians play an important role in the study of many-body quantum systems. Indeed, the multiple inter-nucleon correlations between the A nucleons inside the nucleus can be approximated by A one-body Hamiltonians, whose potentials, acting on a single nucleon, represent the averaged interactions induced by the remaining A − 1 nucleons. As a zeroth-order approximation, one can also deem these potentials as spherical, as the bulk properties of nuclei can be accounted for with spherical potentials.