Related papers: A comment on W. Greiner's "Quantum Mechanics -- An…
An differential equation for wave functions is proposed, which is equivalent to Schr\"{o}dinger's wave equation and can be used to determine energy-level gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this equation is…
There exists a paradigm in which Quantum Mechanics is an exclusively developed theory to explain phenomena on a microscopic scale. As the Planck's constant is extremely small, $h\sim10^{-34}{J.s}$, and as in the relation of de Broglie the…
The Wigner function was introduced as an attempt to describe quantum-mechanical fields with the tools inherited from classical statistical mechanics. In particular, it is widely used to describe the properties of radiation fields. In fact,…
In the paper "The relativistic Doppler effect: when a zero-frequency shift or a red shift exists for sources approaching the observer, Ann. Phys. (Berlin) 523, No. 3, 239-246 (2011), DOI 10.1002/andp.201000099 by C. Wang the use of an…
We analyze recent results concerning the hypothesis of a privileged direction in the space-time that is made by considering a background of the Lorentz symmetry violation determined by a fixed spacelike vector field and the analysis of…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
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.…
We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
Based on the dispersion chain of the Vlasov equations, the paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and…
We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green…
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…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
It is argued that the conclusions obtained by Renninger (Zeitschrift fur Physik 136, 251 (1953)), by means of an interferometer thought experiment, have important implications for a number of still ongoing discussions about quantum…
Scalar theory of quantum electron beam optics, at the single-particle level, derived from the Dirac equation using a Foldy-Wouthuysen-like transformation technique is considered. Round magnetic electron lenses with Glaser and power law…
The so-called Hadamard fractional Brownian motion, as defined in Beghin et al. (2025) by means of Hadamard fractional operators, is a Gaussian process which shares some properties with standard Brownian motion (such as the one-dimensional…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…