Nonlocal interactions: 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 nonlocal potentials without spherical symmetry. For a specified large set of trace‐class interactions it is proved that when, for real k≠0, the Fredholm determinant vanishes, k2 is the energy of a bound state. The point k=0 is examined and the analog of the distinction between zero‐energy bound states and zero‐energy resonances for local central potentials is found. A generalized Levinson theorem is proved.