Related papers: A Minimal Uncertainty Product for One Dimensional …
Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an…
Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized…
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…
We address the time evolution of two- and three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian…
While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate that there is a family of such solutions, which are exact, by employing a null-plane (light-cone) variables…
We analyze relativistic corrections to the wave-packet dynamics of the quantum harmonic oscillator within a perturbative framework. General expressions are derived for the leading-order relativistic contributions to the wave-packet…
In this article we present an exact and unified description of wave-packet dynamics in various 2D systems in presence of a transverse magnetic field. We consider an initial minimum-uncertainty Gaussian wave-packet, and find that its long…
We investigate the time evolution of momentum and position uncertainties for wave packets of arbitrary shape in at most quadratic potentials. We consider all possible cases of potentials and initial conditions. Doing so we see that the…
Using the time-dependent annihilation and creation operators, the invariant operators, for a free mass and an oscillator, we find the coherent-squeezed state representation of a travelling general Gaussian wave packet with initial…
The stability of nuclei is discussed with respect to the width of the Gaussian wave packets within Quantum Molecular Dynamics model. A detailed study is carried out by taking different equations of state (i.e., static soft and hard and the…
We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the `external' momentum related to the motion of the packet center and the `internal' momentum…
We consider wave packets of free particles with a general energy-momentum dispersion relation $E(p)$. The spreading of the wave packet is determined by the velocity $v = \p_p E$. The position-velocity uncertainty relation $\Delta x \Delta v…
It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this…
We discuss on the uncertainty relation (UR) for a closed one dimensional system (circle). In such a system, we cannot use the angle along the circle as a position variable. Otherwise we meet difficulties about the definition of the average…
Normalized wave packets express particles in nature. Their sizes are determined by their interactions with matter, and depend on environments. Nevertheless, these characterize scatterings processes in realistic situations, and govern the…
We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians…
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…
We review critically the main assumptions on which the standard theory of neutrino oscillations is based. We show that all assumptions are realistic, except the so-called "equal momentum assumption", which however is irrelevant. We briefly…
There is renewed attention to whether we can observe the decoherence effect in neutrino oscillation due to the separation of wave packets with different masses in near-future experiments. As a contribution to this endeavor, we extend the…