Related papers: Minimum-Uncertainty Angular Wave Packets and Quant…
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position…
The uncertainty relation for angle and angular momentum has a lower bound which depends on the form of the state. Surprisingly, this lower bound can be very large. We derive the states which have the lowest possible uncertainty product for…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
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 uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…
The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate physical quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose a new…
In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…
We discuss the uncertainty relations in quantum mechanics on noncommutative plane. In particular, we show that, for a given state at most one out of three basic nontrivial uncertainty relations can be saturated. We consider also in some…
The uncertainty relations for angle and angular momentum are revisited. We use the exponential of the angle instead of the angle itself and adopt dispersion as a natural measure of resolution. We find states that minimize the uncertainty…
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty…
The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of…
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution.…
The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the "uncertainty regions'' given by all vectors, whose components are specified by the variances of the three…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…