Related papers: A q-deformed Uncertainty Relation
Certain non-linear relations between the generators of the (q-deformed) Heisenberg algebra are found. Some of these relations are invariant under quantization and $q$-deformation.
The quantum deformation concept is applied to a study of pairing correlations in nuclei with mass 40<A<100. While the nondeformed limit of the theory provides a reasonable overall description of certain nuclear properties and fine structure…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather…
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…
The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The…
We numerically study Barrett-Crane models of Riemannian quantum gravity. We have extended the existing numerical techniques to handle q-deformed models and arbitrary space-time triangulations. We present and interpret expectation values of…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
q-deformed nonlinear field equations are constructed including Klein-Gordon and Maxwell equations. The q-deformation is interpreted as mathematical structure describing specific nonlinearity for which frequency of vibration exponentially…
Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of…
We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space…
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
The notion of conditional entropy is extended to noncomposite systems. The q-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
We study Heisenberg's uncertainty relation relative to a quantum reference frame (QRF). We introduce the QRF as a covariant phase-space observable, show that when described relative to it, position and momentum appear compatible, and derive…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…