Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice
AuthorMuminov, Mukhiddin E.
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CitationMuminov, M. E. (2010). Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice. Theoretical and Mathematical Physics, 164(1), 869-882. http://dx.doi.org/10.1007/s11232-010-0069-4
We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via short-range attractive potentials. We obtain a formula for the number of eigenvalues in an arbitrary interval outside the essential spectrum of the three-particle discrete Schrödinger operator and find a sufficient condition for the discrete spectrum to be finite. We give an example of an application of our results.