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

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Abstract
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.