A century ago, the energy quantization hypothesis and wave-particle duality have been proposed as the foundations of the quantum theory, but still lacking complete theoretical proof and interpretation. For the first time, the "quantized wave particle duality equation" is expressed by a way of physical and mathematical formulas, which simply compose of three factors: the quantized resonant eigenvalue, interaction or transition time, and sum of translational kinetic energy; and accompanied by a full interpretation of the related physical laws. From now on, they are no longer the premise hypothesis of quantum theory, but the inevitable conclusion. The long-term conflict between quantum theory and classical physics has been resolved, which is actually a self-consistent and coherent theoretical system.