Wave-like variables of a classical particle and their connections to quantum mechanics

作者：Yang Chen^*

来源：European Journal of Physics, 2017, 38(1): 015401.

DOI：10.1088/0143-0807/38/1/015401

• wave-like variable
• particle
• classical mechanics
• connections
• quantum mechanics

In many texts, the transition from classical mechanics to quantum mechanics is achieved by substituting the action for the phase angle. The paper presents a different approach to show some connections between classical and quantum mechanics for a single particle for an audience at graduate and postgraduate levels. Firstly, it is shown that a wave equation of action can be derived under the free particle condition and the Legendre transform. The wave-like solutions of the action, Hamiltonian and momentum of the free particle are presented. Using the discrete approximation, the equation of motion of a single particle, in scalar potential field, is obtained in a similar form to Schrodinger's equation. The rest of the paper discusses the propagation, superposition of the wave-like dynamic variables and their connections to quantum mechanics. The superposition of the variables of a particle is generally distinct from the superposition of classical waves (e.g. acoustics). The quantum superposition provides a self-consistent interpretation of the wave-like solutions of the variables. Connections between the classical and quantum relations for corresponding variables are observed from the one-to-one comparisons.

• 出版日期2017-1