@article {2007,
title = {The number of eigenvalues of three-particle Schr{\"o}dinger operators on lattices},
journal = {J. Phys. A 40 (2007) 14819-14842},
number = {arXiv.org;math/0703191v1},
year = {2007},
abstract = {We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.},
doi = {10.1088/1751-8113/40/49/015},
url = {http://hdl.handle.net/1963/2576},
author = {Sergio Albeverio and Gianfausto Dell{\textquoteright}Antonio and Saidakhmat N. Lakaev}
}
@article {2000,
title = {A Remark on One-Dimensional Many-Body Problems with Point Interactions},
journal = {Int. J. Mod. Phys. B 14 (2000) 721-727},
number = {arXiv.org;quant-ph/0001089v1},
year = {2000},
publisher = {World Scientific},
abstract = {The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\\\\delta$-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.},
doi = {10.1142/S0217979200000601},
url = {http://hdl.handle.net/1963/3214},
author = {Sergio Albeverio and Ludwik Dabrowski and Shao-Ming Fei}
}