相关论文: Applications of a Simple Formula
The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…
Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
The purpose of this short note is to exhibit a new connection between the Heisenberg Uncertainty Principle on the line and the Breitenberger Uncertainty Principle on the circle, by considering the commutator of the multiplication and…
The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…
The concept of uncertainty quanta for a general system is introduced and applied to some important problems in physics and mathematics. EPR paradox gives new clue to the further understanding of particle correlation which turns out to be…
This is an article written in a popular science style, in which I will explain: (1) the famous Heisenberg uncertainty principle, expressing the experimental incompatibility of certain properties of micro-physical entities; (2) the Compton…
A solution is given to a conjecture proposed by Y. Wigderson and A. Wigderson concerning a "Heisenberg-like" uncertainty principle. This is an old article already published in 2022.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic…
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…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter $\kappa$ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore…