Related papers: Generalized Radial Uncertainty Product for d-Dimen…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
The uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the paper by two of the present…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
We analyse the universal properties of nonequilibrium steady states of driven Magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the dependence of various phenomenologically important dimensionless constants on the…
Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
We consider the noncommutative algebra which is rotationally invariant. The hydrogen atom is studied in a rotationally invariant noncommutative space. We find the corrections to the energy levels of the hydrogen atom up to the second order…
The position and momentum spreading of the electron distribution of the two-dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb,…
Although real, normalized Gaussian wave packets minimize the product of position and momentum uncertainties, generic complex normalized Gaussian wave packets do not. We prove they minimize an alternative product of uncertainties that…
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the…
We investigate a $D$ dimensional generalization of the Schroedinger-Newton equations, which purport to describe quantum state reduction as resulting from gravitational effects. For a single particle, the system is a combination of the…
The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable…
We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density $n$ and phase $\theta$ variables and…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
We note that presenting Hydrogen atom Schrodinger equation in the case of arbitrary dimensions require simultaneous modification of the Coulomb potential that only in three dimensions has the form Z/r . This was not done in a number of…
We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum…
This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…