Abstract
We consider quantum mechanical three-body systems interacting with two-body potentials that are sufficiently regular locally, decrease faster than r −(2+ ϵ) at infinity, and are such that either one two-body subsystem (at least) has a negative energy bound state, or no two-body subsystem has a zero energy bound state or resonance. (This assumption excludes the possibility of the Efimov effect.) We then prove that (1) the discrete spectrum is finite, (2) the point spectrum has no negative accumulation points. (These results have been proved earlier by Sigal and Yafaev, respectively, by different methods and with slightly different assumptions.)
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