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We prove the uncertainty relation $sigma_T , sigma_E geq hbar/2$ between the time $T$ of detection of a quantum particle on the surface $partial Omega$ of a region $Omegasubset mathbb{R}^3$ containing the particles initial wave function, using the absorbing boundary rule for detection time, and the energy $E$ of the initial wave function. Here, $sigma$ denotes the standard deviation of the probability distribution associated with a quantum observable and a wave function. Since $T$ is associated with a POVM rather than a self-adjoint operator, the relation is not an instance of the standard version of the uncertainty relation due to Robertson and Schrodinger. We also prove that if there is nonzero probability that the particle never reaches $partial Omega$ (in which case we write $T=infty$), and if $sigma_T$ denotes the standard deviation conditional on the event $T<infty$, then $sigma_T , sigma_E geq (hbar/2) sqrt{mathrm{Prob}(T<infty)}$.
We prove a double-inequality for the product of uncertainties for position and momentum of bound states for 1D quantum mechanical systems in the semiclassical limit.
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 angular moment
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method is semidefi
Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the Hilbert-space set
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here w