相关论文: Position Uncertainty Measures on the Sphere

This paper studies the uncertainty principle for spherical $h$-harmonic expansions on the unit sphere of $\mathbb{R}^d$ associated with a weight function invariant under a general finite reflection group, which is in full analogy with the…

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 study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…

In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian…

Composite particles---atoms, molecules, or microspheres---are unique tools for testing joint quantum and general relativistic effects, macroscopic limits of quantum mechanics, and searching for new physics. However, all studies of the free…

Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson,…

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…

Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…

The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…

We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…

The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…

Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…

We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…

Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…

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…

To more flexibly balance between exploration and exploitation, a new meta-heuristic method based on Uncertainty Principle concepts is proposed in this paper. UP is is proved effective in multiple branches of science. In the branch of…

We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…

In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in…

We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…