Universality of the discrete spectrum asymptotics of the three-particle Schrödinger operator on a lattice
M. I. MuminovFaculty of Scince, Universiti Teknologi Malaysia (UTM) 81310 Skudai, Johor Bahru, MalaysiaTulkin H. RasulovFaculty of Physics and Mathematics, Bukhara State University M. Ikbol str. 11, 200100 Bukhara, Uzbekistan
ABI
Annotatsiya
In the present paper, we consider the Hamiltonian H(K), K T 3 := (-; ] 3 of a system of three arbitrary quantum mechanical particles moving on the three-dimensional lattice and interacting via zero range potentials. We find a finite set T 3 such that for all values of the total quasi-momentum K the operator H(K) has infinitely many negative eigenvalues accumulating at zero. It is found that for every K , the number N (K; z) of eigenvalues of H(K) lying on the left of z, z < 0, satisfies the asymptotic relation lim z-0 N (K; z)| log |z|| -1 = U 0 with 0 < U 0 < , independently on the cardinality of .
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