Abstract
The possibility of the coexistence of the diagonal long-range order (DLRO) and the off-diagonal long-range order ( ODLRO), which may be called 'supersolid' state, is discussed in a system of bosons at 0°K. Examples of wave functions are given de scribing the state with only DLRO and with both DLRO and ODLRO. After giving general relationships between the quantum lattice model for a system of bosons and the corresponding spin system, the criterion for the coexistence of DLRO and ODLRO is obtained by using the molecular field approximation for the spin system. The super solid state corresponds to an 'intermediate' state between the antiferromagnetic and spin-flop state in the spin system. The analysis on the basis of this criterion indicates that the bulk solid He 4 is unlikely to become a supersolid, whereas the adsorbed He 4
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