Related papers: Exact solution of the time-dependent harmonic plus…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…
For a time-dependent classical quadratic oscillator we introduce pairs of real and complex invariants that are linear in position and momentum. Each pair of invariants realize explicitly a canonical transformation from the phase space to…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
In the paper Sci. Rep. 8, 8401 (2018), among other things, the Ermakov-Lewis invariant was constructed for the time dependent harmonic oscillator in Koopman-von Neumann mechanics. We point out that there is a simpler method that allows one…
The self-consistent problem of the wave and particle spectrum is formulated and solved for acceleration of particles in a homogeneous magnetic field that varies periodically with time. It follows from the obtained solutions that when…
The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in {\it time-dependent} potentials . In particular, we focus…
In this paper, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We…
The following inverse problem is discussed. A static electromagnetic field generated by a limited system of charges and currents is supposed to be known with its first derivatives at a point somewhere far from the system. This allows to…
We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.
We consider the inverse problem of determining a time-dependent damping coefficient $a$ and a time-dependent potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_x u+a(t,x)\partial_tu+q(t,x)u=0$ in $Q=(0,T)\times\Omega$, with…
In this article, we try to test the influence of the modification of the scalar product, found in the problems of the energy-dependent potential, on the physical properties of the harmonic oscillator in one dimension. For this, we at first…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic…
The nonperturbative guiding-center model provides an exact alternative to full-orbit simulations of charged particle dynamics in situations where traditional guiding-center theory may fail. We demonstrate that the charged particle motion in…
In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schr\"odinger equation and the classical position and momentum variables solving Hamilton's equations. Here…
Analytical solutions are presented for the electromagnetic radiation by an arbitrary pulsed source into a homogeneous time-varying background medium. In the constant-impedance case an explicit radiation formula is obtained for the…
In continuation of our previous study [Phys. Rev. D 99 (2019) 4, 044012], we investigate the motion of charged particles in the $\gamma$-metric. We provide some examples of curled trajectories in the equatorial plane and escape trajectories…
A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
It is impossible to obtain accurate frequencies from time signals of a very short duration. This is a common believe among contemporary physicists. Here I present a practical way of extracting energies to a high precision from very short…