Related papers: A Characteristic Particle Length
It is known that Schr\"odinger equation fails in describing the dynamics of highly energetic particles. We propose to quantify this lack of Lorentz covariance by evaluating the probability for a particle to be measured outside the set of…
We investigate spectral properties of limit-periodic Schr\"odinger operators in $\ell^2(\Z)$. Our goal is to exhibit as rich a spectral picture as possible. We regard limit-periodic potentials as generated by continuous sampling along the…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
Even though there have been the various varying speed of light (VSL) cosmology models, they remain out of the mainstream because of their possible violation of physics laws built into fundamental physics. In order to be the VSL as a viable…
Propagation of relativistic particles in the Schwarzschild gravitational field is studied. Particles emitted radially outward with speed at infinity exceeding c/2^0.5 are observed to be accelerated in the gravitational field by a distant…
The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time,…
We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising…
We determined the characteristic variability time scales (\Delta t_p) of 410 bright and long GRBs, by locating the peaks of their Power Density Spectra, defined and calculated in the time domain. We found that the averaged variability time…
We analyze a sample of bright short bursts from the BATSE 4B-catalog and find that many short bursts are highly variable ($\delta t_{min}/T\ll 1$, where $\delta t_{min}$ is the shortest pulse duration and T is the burst duration). This…
We characterize observable sets for 1-dim Schr\"{o}dinger equations in $\mathbb{R}$: $i \partial_t u = (-\partial_x^2+x^{2m})u$ (with $m\in \mathbb{N}:=\{0,1,\dots\}$). More precisely, we obtain what follows: First, when $m=0$,…
We argue that a consistent definition of the velocity of a particle in generalizations of special relativity with two observer-independent scales should be independent from the mass of the particle. This request rules out the definition…
With the simplest proof ever, we justify the significance of quantum-gravity in non-relativistic quantum mechanics together with the related theories and experiments. Since the de Broglie wave length is inverse proportional to the mass, it…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
The high-temperature limit of Standard Model generated by the contractions of gauge groups is discussed. Contraction parameters of gauge group $SU(2)$ of Electroweak Model and gauge group $SU(3)$ of Quantum Chromodynamics are taken…
Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry…
Lorentz ordering (causality) implies the following rule: for any given energy p0 of a system there is a certain interval c0 on x0 so that their product is the Lorentz ordering constant L It means p0c0 = L. The constant L=hc. Hence Planck…
We consider Higgs-Higgs scattering in a minimal Higgs model with strong coupling which leads to the Higgs as a bound state. The partial wave amplitude is unitarized using general principles of analyticity. We find lambda(m_H)/16pi is…
In the gauge theory context, a definition of branching ratios and partial widths of unstable particles is proposed that satisfies the basic principles of additivity and gauge independence. A simpler definition, similar to the conventional…
A spinless nonrelativistic quantum particle on the curved surface of a homogeneous spherocylindrical capsule is considered. We apply Costa's formalism to solve the Schr\"{o}dinger equation with only a confined potential forcing the particle…