What is the physical meaning of the quantum wave function?

About a hundred years ago, there was a famous debate between Bohr and Einstein: Does the quantum wave function of an electron have a physical meaning beyond probability? This question is still open today. This work proposes a new theoretical framework to address the above question. Our approach is that, based on observations that photons and electrons have similar wave properties, we hypothesize that both of them are quantized excitation waves of the vacuum, the physical properties of which can be modelled based on the Maxwell theory. Using the method of Helmholtz decomposition, we showed that the wave function of the particle is associated with an electric vector potential called “Z”, which plays the role of basic field for the excitation wave. Using this framework, the quantum wave equations of electron can be derived directly from the Maxwell theory.