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In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the…
We present a local-realistic description of both wave-particle duality and Bohmian trajectories. Our approach is relativistic and based on Hamilton's principle of classical mechanics, but departs from its standard setting in two respects.…
Using Feynman's representation of the quantum evolution and considering a quantum particle as a matter field (continuous medium), it is shown that individual particles of the field have unique paths of the motion. This allows describing…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse,…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled non-linear equations that can be…
Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
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…
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…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
The "main road" open by de Broglie's and Schroedinger's discovery of matter waves and of their eigen-functions branched off, as is well known, into different "sub-routes". The most widely accepted one is Standard Quantum Mechanics (SQM),…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
We study a special kind of semiclassical limit of quantum dynamics on a circle and in a box (infinite potential well with hard walls) as the Planck constant tends to zero and time tends to infinity. The results give detailed information…
We consider a basic model of the lossless interaction between a moving two-level atom and a standing-wave single-mode laser field. Classical treatment of the translational atomic motion provides the semiclassical Hamilton-Schrodinger…
Based on an observation that the basic mode of a common microwave waveguide is a solution to the Klein-Gordon equation, quantum mechanics is modeled as the wave-function propagated inside a waveguide. The guide width is determined by the…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large…