Related papers: Uncertainty relation for angle from a quantum-hydr…
Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum…
Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. Moreover, a notion of operator-valued variance is…
Analyzing Heisenberg--Robertson (HR) and Schr\"{o}dinger uncertainty relations we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard…
Introductory courses on quantum mechanics usually include lectures on uncertainty relations, typically the inequality derived by Robertson and, perhaps, other statements. For the benefit of the lecturers, we present a unified approach --…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
We have obtained the uncertainty relations for arbitrary states of the hydrogen atom. It is shown that the minimal value of the uncertainty relation is attained for the circular Rydberg states.
Gaussian distribution of a quantum state with continuous spectrum is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $\hat x$ and $\hat p$, quantum entropic…
Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we…
A striking feature of standard quantum mechanics is its analogy with classical fluid dynamics. In particular it is well known the Schr\"{o}dinger equation can be viewed as describing a classical compressible and non-viscous fluid, described…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
The curvelet transform is a special type of wavelet transform, which is useful for estimating the locations and orientations of waves propagating in Euclidean space. We prove an uncertainty principle that lower-bounds the variance of these…
Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
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…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…