Related papers: Precanonical Quantization and the Schroedinger Wav…
The Wigner function plays a central role in QCD as a phase space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent…
According to classical non-relativistic Schr\"odinger equation, any local perturbation of wave function instantaneously affects all infinite region, because this equation is of parabolic type, and its solutions demonstrate infinite speed of…
In this paper, we establish orbital stability results for \textit{cnoidal} periodic waves of the cubic nonlinear Klein-Gordon and Schr\"odinger equations in the energy space restricted to zero mean periodic functions. More precisely, for…
We study one of the interesting properties of the electromagnetic wave propagation in the curved Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum…
Recently proposed quantization in field theory based on an analogue of Hamiltonian formulation which treats space and time on equal footing (the so-called De Donder-Weyl theory) is applied to General Relativity in metric variables. We…
The aim of the article to clarify the status of Shapiro plane wave solutions of the Schr\"odinger's equation in the frames of the well-known general method of separation of variables. To solve this task, we use the well-known cylindrical…
We consider a mass-less manifestly covariant {\it linear} Schr\"odinger equation. First, we show that it possesses a class of non-dispersive soliton solution with finite-size spatio-temporal support inside which the quantum amplitude…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…
We briefly review results on Colombeau type generalized solutions to the Cauchy problem for linear Schr\"odinger-type equations with non-smooth principal part and their compatibility with classical and distributional solutions. In the main…
Starting on the basis of $q$-symmetric oscillator algebra and on the associate $q$-calculus properties, we study a deformed quantum mechanics defined in the framework of the basic square-integrable wave functions space. In this context, we…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
Existence and bifurcation results are derived for quasi periodic traveling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial type potentials. Variational tools are used. Several concrete…
Careful exploration of the idea that equation for radial wave function must be compatible with the full Schrodinger equation shows appearance of the delta-function while reduction of full Schrodinger equation in spherical coordinates.…
We discuss the limits of the photon wavefunction (PWF) formalism, which is experiencing a revival in these days from the new practical applications in photonics and quantum optics. We build a Dirac-like equation for the PWF written in a…
A study on the notion of covariant derivatives in flat and curved space-time via It\^o-Wiener processes, when subjected to stochastic processes, is presented. Going into details, there is an analysis of the following topics: (i) Besov…
For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the…
With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant…