NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2016, 7 (5), P. 880–887
Spectral properties of a two–particle hamiltonian on a d-dimensional lattice
M. I. Muminov – Universiti Teknologi Malaysia (UTM), 81310 Skudai, Johor Bahru, Malaysia; firstname.lastname@example.org
A. M. Khurramov – Department of Mechaniical and Mathematics, Samarkand State University, Uzbekistan; email@example.com
A system of two arbitrary quantum particles moving on d-dimensional lattice interacting via some attractive potential is considered. The number of eigenvalues of the family h(k) is studied depending on the interaction energy of particles and the total quasi-momentum k∈Td (Td – d-dimensional torus). Depending on the interaction energy, the conditions for h(0) that has simple or multifold virtual level at 0 are found.
Keywords: two-particle hamiltonian, virtual level, multiplicity of virtual level.