Theory of Wave Propagation of Particle Based on the Frameworks of Newtonian Mechanics and Classic Quantum Mechanics

In this paper, based on the paper of Schrödinger, “ An Undulatory Theory of the Mechanics of Atoms and Molecules”, and the theory of de Broglie wave-particle duality, authors analyze the motion of a material point both in the framework of Newtonian Mechanics and in the framework of Classic Quantum Mechanics.

First, in the framework of Newtonian Mechanics, with the help of Hamilton Principal and Hamilton-Jacobi Equation, we can prove that the wave equation from the theory of de Broglie is a displacement equation.

Secondly, in the framework of Classic Quantum Mechanics, with the help of Hamilton Principle and Hamilton-Jacobi Equation, Schrödinger Equation is obtained. So it is concluded that Schrödinger Equation is a displacement equation and wave function is a displacement function.

Mathematically, it is first time found that the collapse of wave function only takes place in the same types of particles. There exists a boundary between Newton Mechanics and Quantum Mechanics from the point of view of energy. It can be reasonably inferred that the randomness of photon or electronic in Double Slot Test is caused by one type or multiple types of particles, which are mysterious and unknow for human being up to now.



Keywords: Wave-Particle Duality, Schrödinger Equation, Wave Function, Wave Function Collapse