Dual quantum mechanics and its electromagnetic analog

TL;DR

This paper introduces a dual quantum framework with scalar and vector wavefunctions, deriving a quantum Telegraph equation and an electromagnetic analogy, revealing new insights into particle behavior, energy relations, and creation-annihilation processes.

Contribution

It presents a novel dual quantum equation set and an electromagnetic analogy, leading to quantized Maxwell's equations and new particle energy and force relations.

Findings

Derivation of a quantum Telegraph equation for particles.

Establishment of an electromagnetic analogy with Maxwell's equations.

Identification of a dual Lorentz-like force and dissipative quantum forces.

Abstract

An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation keeping the form of the particle fixed but decaying its amplitude. An analogy with Maxwellian equations is presented. Massive electromagnetic field will satisfy a quantum Telegraph equation instead of a pure wave equation. This equation resembles the motion of the electromagnetic field in a conducting medium. With a particular setting of the scalar and vector wavefunctions, the dual quantum equations are found to yield the quantized Maxwell's equations. The total energy of the particle is related to the phase velocity ($v_p$) of the wave representing it by $E=p\,|v_p|$\,, where $p$ is the matter wave momentum. A particular solution which describes the process under which the particle undergoes a creation and annihilation is derived. The force acting on the moving particle is expressed in a dual Lorentz-like form. If the particle moves like a fluid, a dissipative (drag) quantum force will arise.