On the Bogoliubov type asymptotics of the boson spectrum for the N-particles Schrödinger operator with binary potential when density tends to infinitum

A new asymptotic method is proposed for calculation of boson spectral series and corresponding asymptotic eigenfunctions for the spinless N-particles Schrödinger equation when N tends to infinitum but the physical parameters and the volume are fixed, that is the density of the system tends to infinitum. For the low levels eigenvalues the Bogoliubov spectrum is obtained just as in the case of small density.The asymptotic formulas are rigorously proved.