In this paper, we explore the theory of the equation of state from the view point of Ihm-Song-Mason (ISM) equation of state, which has been derived on the basis of statistical mechanical perturbation theory, and is characterized by three temperature dependent parameters, alpha, b, B-2, and a free parameter Gamma. This equation is applied well to non-polar fluids in subcritical and supercritical regions and to molten alkali metals. We present results that show Gamma varies slightly with temperature. Among the nobles group, Gamma values are quite the same and are correlated except He, which deviates so much even no moderate correlation is seen. In the alkali metals group, Gamma values are roughly the same for K, Rb, and Cs but are different for Li and Na. We have previously shown that Gamma conforms to B-2, the second virial coefficient, and thus to the nature of the particular fluid system. These observations plus the discussion on quantum mechanical law of corresponding states suggest that the ISM equation of state stands as an analytical equation of state which explicitly incorporates quantum effects by the parameter Gamma. Then, we suggest a law of corresponding states as p* =p*(v*, T*, Gamma) where, asterisks stand for reduced pressure, volume, and temperature, respectively.