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Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice. (English. Russian original) Zbl 1319.81038

Theor. Math. Phys. 182, No. 3, 381-396 (2015); translation from Teor. Mat. Fiz. 182, No. 3, 435-452 (2015).
Summary: We consider a system of three arbitrary quantum particles on a three-dimensional lattice interacting via attractive pair-contact potentials and attractive potentials of particles at the nearest-neighbor sites. We prove that the Hamiltonian of the corresponding three-particle system has infinitely many eigenvalues. We also list different types of attractive potentials whose eigenvalues can be to the left of the essential spectrum, in a gap in the essential spectrum, and in the essential spectrum of the considered operator.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
82D25 Statistical mechanics of crystals
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