BIRMAN-SCHWINGER PRINCIPLE FOR TWO-PARTICLE DISCRETE SCHRÖDINGER OPERATORS ON LATTICES
Keywords:
discrete Schrödinger operators, quantum mechanical two-particle, Birman-Schwinger principle, system, hamiltonians.Abstract
We consider a system of two identical bosons moving on the
hypercubic lattice , and interacting through attractive short range
potentials µV (µ > 0) and the two-particle Schrödinger operators (k)- , k associated to the system, where is the d - dimensional torus. We
study the Birman-Schwinger principle for two-particle Schrödinger operators.
References
S.Albeverio, S. N. Lakaev,K. A. Makarov, Z. I. Muminov: The Threshold Effects for the Two-particle Hamiltonians on Lattices, Comm.Math.Phys. 262(2006), 91--115
Albeverio S., Lakaev S. N., and Muminov Z. I.: Schrödinger operators on lattices. The Efimov effect and discrete spectrum asymptotics, Ann. Henri Poincaré. 5, 743--772 (2004).
Albeverio, S.N. Lakaev and A.M. Khalkhujaev: Number of Eigenvalues of the ThreeParticle Schrodinger Operators on Lattices, 18 (2012), 18pp. 387-420 4. V. Bach, W. de Siqueira Pedra, S. Lakaev:Bounds on the Discrete Spectrum of Lattice Schrödinger Operators Preprint mp-arc 10-143.
