Noncentral potentials: The generalized Levinson theorem and the structure of the spectrum

Fredholm theory is applied to the Lippmann–Schwinger equation for noncentral potentials. For a specified wide class of potentials it is proved that the modified Fredholm determinant cannot vanish for real k≠0. The point k=0 is examined and the analog of the distinction between zero-energy bound states and zero-energy resonances for central potentials is found. A generalized Levinson theorem is proved.