At the outset it seems hopeless to expect that there is such a thing as a rational wave equation whose solutions can only be rational functions. However, if a theory can be developed then rational wave equation can be used to solve problems of space-time quantization. As the application of a theory of partial differentiation and partial differential equations, the wave equation, the heat equation, and the Laplace equation are all indispensable. The theory of partial differential is really a mathematical theory of describing natural processes of continuous variation of space, of time, and of course of space-time. The more important question is why can a true theory of continuity be able to describe the discreteness or discontinuity of reality? The answer can be given by the following illustration, which was first noted by Newton while he was still developing differential calculus in the 1600s where and when he was strolling along the seashore and took an instantaneous snapshot of the approaching solitons. This mental picture shows a regular pattern of highs and lows in an instant of time that is periodic vertical motion in space with respect to distance. However, if Newton stays in the water, he can feel the rise and fall of the water as each constant soliton passes by, seeing periodic vertical motion in time. These instantaneous changes in space and in time cannot be simultaneously observed. Observing one, presumed no information for the other, vice versa. Nonetheless, the comparison of double observations of space and time gives the square of the speed of each observation. The product of two observations gives the square of relativistic energy. This square of energy is used to describe the quantum evolution of each wavefunction as studied in both quantum mechanics and quantum field theory. The former studies the evolution of single wavefunction and its linear superposition, while the latter studies the product of multiple numbers of wavefunctions of which total space-time quantization gives physical descriptions using symmetric singular Hadamard matrices representing the square of zero-point energies of the quantum vacuum fluctuations and normalized by the rational equation ����=(��-��)�� where ��=1 and both �� and �� are rational numbers.