Related papers: Control of particle propagation beyond the uncerta…
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines…
The dynamics of a particle propagating in free space is described by its position and momentum, where quantum mechanics prohibits the simultaneous identification of two non-commutative physical quantities. Recently, a lower bound on the…
Quantum particles move in strange ways, even when they propagate freely in space. As a result of the uncertainty principle, it is not possible to control the initial conditions of particle emission in such a way that the particle will…
The uncertainty principle suggests a quantitative trade-off between the control of position and the control of momentum in particle propagation. However, a superposition of two states with very different uncertainty trade-offs introduces an…
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. In the picture used, the transmitted wave packet results from interference between the copies of the freely…
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…
Quantum theory implies, and empirical evidence confirms, that while particles $\textit{can}$ exhibit wave-like behavior in interferometric experiments, this behavior is so limited as $\textit{not}$ to allow for third- and higher-order…
An interference experiment with entangled particles is theoretically analyzed, where one of the entangled pair (particle 1) goes through a multi-slit before being detected at a fixed detector. In addition, one introduces a mechanism for…
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 develop a framework to test the Equivalence Principle (EP) under conditions where the quantum aspects of nature cannot be neglected, specifically in the context of interference phenomena with unstable particles. We derive the…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions…
This paper presents the uncertainty related to position and momentum localization of a quantum state in terms of entropic uncertainty relations. We slightly improve the inequality given in [Phys. Rev. A 74, 052101 (2006)] and introduce a…
The existence of precise particle trajectories in any quantum state is accounted for in a consistent way by allowing delocalization of the particle charge. The relativistic mass of the particle remains within a small volume surrounding a…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
Bell experiments have confirmed that quantum entanglement is an inseparable correlation but there is no faster-than-light influence between two entangled particles when a local measurement is performed. However, how such an inseparable…
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite…
The precession protocol involves measuring $P_3$, the probability that a uniformly precessing observable (like the position of a harmonic oscillator or a coordinate undergoing spatial rotation) is positive at one of three equally spaced…
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's…