Related papers: Wave-particle duality and the zitterbewegung
A 6-component "wave function" (not field, but S-matrix interpretable) for a massive spin-1 particle parallels the Dirac "chirality-doubled" 4-component wave function for a spin-1/2 particle, by pairing two wave functions for same spin but…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, specified by the probability…
Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and…
A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing…
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various…
We derive a general and simple expression for the time-dependence of the position operator of a multi-band Hamiltonian with arbitrary matrix elements depending only on the momentum of the quasi-particle. Our result shows that in such…
The study of this paper demonstrates that electron has Dirac delta like internal momentum (u,p_{{\theta}}), going round in a circle of radius equal to half the reduced Compton wavelength of electron with tangential velocity c. The circular…
A basic problem in the relativistic quantum Hamilton-Jacobi theory is to understand whether it may admit superluminal solutions. Here we consider the averaging of the speed on a period of the oscillating term which is similar to Dirac's…
We consider non-relativistic point-particles coupled to Einstein gravity and their canonical quantization. From the resulting Wheeler-DeWitt wave equation we determine a quantum version of geometrodynamics, where the coupled evolution of…
The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and…
We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the…
The proposed paper presents the unobserved inadequacies in de Broglie's concepts of wave-particle duality and matter waves in the year 1923. The commonly admitted quantum energy or frequency expression h{\nu}={\gamma}mc2 is shown to be…
Zitterbewegung (ZBW), the trembling motion predicted by the Dirac equation, has long remained unobservable in free electrons due to its sub-Compton scale. We elaborately construct a relativistic vortex electron wave packet as a coherent…
In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited…
A short review of special relativistic dynamics describing a particle acted upon by an arbitrary conservative external force is presented. If the mass of the particle is zero and the force is central then the equations of motion turn out to…
Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle's path inside the interferometer. This idea has been…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
We introduce a dual wave-particle macroscopic system, where a bead oscillator oscillates in an elastic medium which obeys the Klein-Gordon equation. This theoretical system is mostly inspired by bouncing droplets experiments and bead…