Spectra of Hamiltonians with nonlocal potentials

Abstract

We present a method for determining the elements of the spectrum of Hamiltonians describing a class of confined systems with nonlocal potentials using Green’s functions. Some of the elements of the spectrum of these Hamiltonians coincide with some of the elements of the spectrum of a particle in a box system, which signifies that certain systems with nonlocal potentials may, with respect to their characteristic energies, appear to be particle in a box systems, with the true nature of the system being revealed by fully determining the characteristic energies of this system.