The pressure-temperature phase diagram of BaTiO₃ was investigated by using a modification of the standard Landau potential to take account of quantum saturation of the order parameter. At low temperatures, each phase boundary bends sharply down, and this non-linear behavior is associated with quantum mechanical effects. Saturation temperature θ_s characterizes the extent of quantum mechanical, and is related to the extent to which changes in the hard phonon modes influence the transition mechanism.