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The examples of rhythmical signals with variable period are considered. The definition of periodic function with the variable period is given as a model of such signals. The examples of such functions are given and their variable periods…
It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle <S>. This result follows from the fact that in the classical limit h=0 the Schroedinger…
Erwin Schrodinger (1939) proved that quantum wave functions coevolve with the curved spacetime of the Friedmann universe. Schrodinger's derivation explains the Hubble redshift of photons in an expanding universe, the energy changes of…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
It has been suggested that the nonlinear Schr\"odinger-Newton equation might approximate the coupling of quantum mechanics with gravitation, particularly in the context of the M{\o}ller-Rosenfeld semiclassical theory. Numerical results for…
The complete solutions of the Schr\"odinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is with the…
Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave…
Lorentz-covariant harmonic oscillator wave functions are constructed from the Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and Ravndal for a two-body bound state. The wave functions are not invariant but…
Wave-particle duality as one of the expression of Bohr complementarity is a significant concept in the field of quantum mechanics. Quantitative analysis of wave-particle duality aims to establish a complementary relation between the…
In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…
Space-time-modulated systems have attracted significant interest over the past decade due to their ability to manipulate electromagnetic waves in unprecedented ways. Here, we introduce a new type of space-time-modulated structure, the…
With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by…
This paper is devoted to three topics. First, proving a measurability theorem for multifunctions with values in non-metrizable spaces, which is required to show that solutions to stochastic wave equations with interval parameters are random…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
Here we study a new kind of linear integral equations for a relativistic quantum-mechanical two-particle wave function $\psi(x_1,x_2)$, where $x_1,x_2$ are spacetime points. In the case of retarded interaction, these integral equations are…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
A semilinear wave equation with slowly varying wave speed is considered in one to three space dimensions on a bounded interval, a rectangle or a box, respectively. It is shown that the action, which is the harmonic energy divided by the…
The subject of this paper is multigrid solvers for Helmholtz operators with large wave numbers. Algorithms presented here are variations of the wave-ray solver which is modified to allow efficient solutions for operators with constant,…