An expression for the dynamical susceptibility is derived for a system of electrons in a narrow s-band with strong correlations. The interaction considered is a short-range repulsive one which acts only between electrons with different spins on the same Wannier site. A sequence of equations for the two-time Green's function related to the dynamical susceptibility is decoupled by a method like that of Hubbard so as to include the correlation at the same Wannier site. Compared with the RPA result, the obtained dynamical susceptiblity is characterized by the reduction of the interaction energy to the order of the band width and the narrowing of one-electron energy band in the strong correlation limit. A condition for paramagnetic instability and spin wave dispersions derived from the denominator of the susceptibility are discussed.
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Akio Sakurai (1968) studied this question.