Wave–particle duality revisited

Abstract

Rewriting the wavefunction ψ, representing a quantum particle, in terms of real scalar and vector functions, R0 and vector R→, in the unified quantum mechanics equations gives more insight about the wave–particle dynamics. This expression is found to embody the wave–particle nature of a quantum particle. This reveals that the particle is composed of massless and massive fields. The scalar R0 and vector R→ functions represent the massive fields satisfying the quantum telegraph equation, whereas the phase S represents a massless field. The three functions are coupled to each other. Interestingly, the product SR0 satisfies the telegraph equation too. This product is found to represent the potential energy of particle field and that the product SR→ represents its momentum. Sometimes, the particle behaves like a fluid (wave) with a specific conserved energy–momentum tensor. This is a manifestation of the anticipated duality of a quantum particle. Besides the quantum potential proposed by Bohm, we have found an additional potential that depends solely on the phase of the wavefunction. The splitting of the wavefunction yields the Hamilton–Jacobi equation whose Hamiltonian is that of a massless relativistic Dirac particle, where the Dirac matrix α→ connects the vector field to the real one. The quantum potential disappears in the new formalism of quantum mechanics. The Bohmian Dirac quantum mechanics yields a relativistic Hamilton–Jacobi equation and the continuity equation. Application of the Bohmian method to Maxwell’s equations shows that the electromagnetic field exhibits the particle–wave duality. It is found that when the photon behaves as matter it does that like a massless Dirac particle.