Related papers: About Heisenberg Uncertainty Relation (by E.Schrod…
We provide an analytical proof of the entropic uncertainty relations presented by de Vicente and Sanchez-Ruiz in [Phys. Rev. A 77, 042110 (2008)] and also show that the replacement of Eq. (27) by Eq. (29) in that reference introduces…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture;…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schr\"odinger on foundational issues in quantum mechanics into a quantitative prediction of a new…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…
In this comment, we point out some shortcomings in two papers "Fractional quantum mechanics" [Phys. Rev. E 62, 3135 (2000)] and "Fractional Schroedinger equation" [Phys. Rev. E 66, 056108 (2002)]. We prove that the fractional uncertainty…
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in…
The status of the uncertainty relations varies between the different interpretations of quantum mechanics. The aim of the current paper is to explore their meanings within a certain neo-Everettian many worlds interpretation. We will also…
This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in…
Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…
Heisenberg's uncertainty principle was originally formulated in 1927 as a quantitative relation between the "mean error" of a measurement of one observable and the disturbance thereby caused on another observable. Heisenberg derived this…
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing…
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the EPR paradox.…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
The Robertson's formulation of the uncertainty relation is the most widely accepted form of the Heisenberg uncertainty relation (HUR). It gets modified when we consider it for entangled particles. But this formulation does not consider the…
The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…