Related papers: Wave Packets in Discrete Quantum Phase Space
The spreading of quantum mechanical wave packets is studied in two cases. Firstly we look at the time behavior of the packet width of a free particle confined in the observable Universe. Secondly, by imposing the conservation of the time…
We study the Generalized Uncertainty Principle (GUP) modified time evolution for the width of wave-packets for a scalar potential. Free particle case is solved exactly where the wave-packet broadening is modified by a coupling between the…
We discuss some of the properties of the `collision' of a quantum mechanical wave packet with an infinitely high potential barrier, focusing on novel aspects such as the detailed time-dependence of the momentum-space probability density and…
The broadening of one-dimensional Gaussian wave packets is presented in all textbooks on quantum mechanics. It is used to elucidate Heisenberg's uncertainty relation. The behaviour on a lattice is drastically different if the amplitude…
Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a…
An improved criterion for distinguishing conditions in which classical or quantum behavior occurs is developed by comparing classical and quantum mechanical measures of size while incorporating spatial and temporal restrictions on wave…
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…
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through…
We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting…
In this study, potential scatterings are formulated in experimental setups with Gaussian wave packets in accordance with a probability principle and associativity of products. A breaking of an associativity is observed in scalar products…
The paper first discusses theoretically the off-resonance selective excitation method that is dependent on the atomic internal states and used to generate approximately a standard coherent state of harmonic oscillator. The coherent average…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…
Any pure quantum state can be equivalently represented by means of its wave function psi(q) or of the Fermi function g_F(q,p), with q and p coordinates and conjugate momenta of the system under investigation.We show that a Gaussian wave…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
It is shown that the initial conditions in the quasi-Heisenberg quantization scheme can be set at the initial cosmological singularity per se. This possibility is provided by finiteness of some quantities, namely momentums of the dynamical…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…