Abstract
The procedure of solving equations for the generalized density matrix method is demonstrated in the Lipkin-Meshkov-Glick model. Self-consistency and adequacy of the basic equations of the method are shown. To determine the collective spectrum of the system, we used the quasiclassical approximation with the excitation of the system determined practically in the whole variation range of the nucleon-nucleon interaction value including the transitional region. As a limiting case, the random phase approximation and its validity domain have been obtained. The equivalence of one of the equations of the method, namely the equation [R, Q + 1 2 τ] = 0 , to the normalization condition of the generalized density matrix R 2 = R has been proved.
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