Abstract
Under the assumption that the ground-state wave function is expressed as a product of pair functions, the expectation value of the ground-state energy is rigorousJy expressed in terms of the pair distribution function. An integra-differential equation is derived for the pair distribution function from the variational principle that the expectation value of the energy is minimum. It is pointed out that the expression for the energy and the integra differential equation become identical with those c1eri vecl by Abe if the hyper-netted chain (HNC) approximation is introduced. It is proved that the HNC approximation is compatible with the virial theorem. The nature of the formulas is investigated by applying them to some cases that have been investigatecl by other theories. It is suggested that the present theory may in ge_neral predict the phonon-like excitations.
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