Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice

Details Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice

Feb 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008tmp...154..311m&link_type=abstract

Theoretical and Mathematical Physics, Volume 154, Issue 2, pp.311-318

Mathematics

Mathematical Physics

Resonance, Two-Particle Sub-Hamiltonian, Discrete Spectrum, Variation Principle

Scientific paper

We consider a system of three quantum particles interacting by pairwise short-range attraction potentials on a three-dimensional lattice (one of the particles has an infinite mass). We prove that the number of bound states of the corresponding Schrödinger operator is finite in the case where the potentials satisfy certain conditions, the two two-particle sub-Hamiltonians with infinite mass have a resonance at zero, and zero is a regular point for the two-particle sub-Hamiltonian with finite mass.

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