Related papers: Quantum mechanical Gaussian wavepackets of single …
It was also shown recently that GUP predicts potentially measurable corrections to the `doubling time' of freely moving Gaussian atomic and molecular wavepackets with a favorable combination of three parameters, {\it e.g.} mass, initial…
The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy…
In order to reduce the Klein-Gordon equation (with minimal coupling), we introduce a generalization of the so-called "mode solutions" that are well-known in the special case of a Robertson-Walker universe. After separation of the variables,…
The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…
The nonlinear quantization of the domain wall (relativistic membrane of codimension 1) is considered. The membrane dust equation is considered as an analogue of the Hamilton-Jacobi equation, which allows us to construct its quantum…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
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…
Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On other…
Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…
The charge spreading of ground and excited states of Klein-Gordon particles moving in a Coulomb potential is quantitatively analyzed by means of the ordinary moments and the Heisenberg measure as well as by use of the most relevant…
We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…
Simulation and analysis of multidimensional dynamics of a quantum non-Hmeritian system is a challenging problem. Gaussian wavepacket dynamics has proven to be an intuitive semiclassical approach to approximately solving the dynamics of…
A procedure for obtaining correlation function densities and wavefunctionals for quantum gravity from the Donaldson polynomial invariants of topological quantum field theories, is given. We illustrate how our procedure may be applied to…
The behavior of quantum speed limit time (QSLT) for a single free spin $-1/2$ particle described by Gaussian wavepackets in the framework of relativity under dephasing noise is investigated. The dephasing noise acts only on the spin degrees…
For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides…
Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic…
The weak equivalence principle of gravity is examined at the quantum level in two ways. First, the position detection probabilities of particles described by a non-Gaussian wave-packet projected upwards against gravity around the classical…
A new mechanism of particle acceleration, based on the resonant interaction of a classical electromagnetic wave (EM) with a quantum wave (associated with a relativistic particle), is explored. In a model illustrative calculation, we study…
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
Let $B$ be a spatial region of width $2R$ and $\Phi$ a Klein-Gordon wave packet localized in $B$ at time zero. We show the inequality $S \leq 2\pi R E$; here, $S$ is the entropy of $\Phi$ contained in a region $B$, and $E$ is the energy…