Modelling Wave-Particle Duality of Classical Particles and Waves

Wave-particle duality is the fundamental phenomenon of particles and fields in quantum mechanics. In the past, the trajectory-like (particle-like) behaviour and wave-like behaviour has been considered separately. In this article, a superimposed model is derived to characterise wave-particle duality of classical particles. The superimposed model reflects an invariant mathematical structure (analogous variables and differential equations) from classical mechanics, classical field theories and quantum mechanics. Its analytical solution carries trajectory-like property (phase-independent) and wave-like property (phase-dependent) of particles that is consistent with to Schrodinger’s picture. Subsequently, the presented model is applied to model duality of classical waves in electromagnetism, acoustics and elasticity. The analysis implies the existence of quantum effects of classical waves at macroscopic scale. It predicts quantum picture on energy and momentum exchange between classical particles and waves. As seen in the model, wave-particle duality reflects inherent and indispensable characteristics of classical objects.