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The Hamiltonian description of the self-consistent interaction between an electromagnetic plane-wave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model…
In this work, it is demonstrated that there is an additional origin of the electric potential energy of an electron orbiting a nuclei that can be, alternatively to that associated to the elementary `static' charge of the electron as…
If a wave function does not describe microscopic reality then what does? Reformulating quantum mechanics in path-integral terms leads to a notion of "precluded event" and thence to the proposal that quantal reality differs from classical…
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…
We briefly report on a recent proposal (Fiore in J Phys A Math Theor 51:085203, 2018) for simplifying the equations of motion of charged particles in an electromagnetic (EM) field $F^{\mu\nu}$ that is the sum of a plane travelling wave…
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
Starting from the quantum hydrodynamic model and transforming to the coupled driven pseudoforce system the plasmonic excitations of electron beam with arbitrary degree of degeneracy are studied. Using the conventional normal-mode analysis a…
We study the effects of the electromagnetic vacuum on the motion of a nonrelativistic electron. First, we derive the equation of motion for the expectation value of the electron's position operator. We show how this equation has the same…
As a realistic model of a quantum system of matter, this paper investigates the gravitational-wave effects on a hydrogen-like atom. By formulating the tetrad formalism of linearized gravity, we naturally incorporate the gravitational-wave…
The new quantum state of a relativistic electron in a vacuum is described. It corresponds to an electron moving freely along a certain direction and being self-localized in a plane which is transverse to its momentum. This semi-localized…
A classical circularly polarized electromagnetic wave carries angular momentum, and represents the classical limit of a photon, which carries quantized spin. It is shown that a very similar picture of a circularly polarized coherent wave…
Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they…
A nonadiabatic scheme for the description of the coupled electron and nuclear motions in the ozone molecule was proposed recently. An initial coherent nonstationary state was prepared as a superposition of the ground state and the excited…
We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with non--symmetrical hydrogen bonds. In our approach, the masses of the hydrogen nuclei are scaled…
Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any…
We explain the approximate nature of particle trajectories in Bohm's quantum mechanics. They are streamlines of a superfluid in Madelung's reformulation of the Schr\"{o}dinger wave function, around which the proper particle trajectories…
Motivated by a revision of the classical equations of electromagnetism that allow for the inclusion of solitary waves in the solution space, the material collected in these notes examines the consequences of adopting the modified model in…
Angular momentum and torque are important principles for basic and applied physics on any spatial scales, for example, in elementary particles, cold gases, optical tweezers, quantum information technology, metamaterials, gyroscopes or…