Related papers: Heisenberg, uncertainty, and the scanning tunnelin…
It is well known that the problem of divergence in the physical interpretation of quantum mechanics originating from the uncertainty principle has not yet been resolved. Attempting to clear the constraints and confusion of this situation…
It is considered constraints imposed by the quantum mechanics on the measurement of the density of the electromagnetic energy. First, the energy of the electromagnetic wave and the volume (time) are bound with the Heisenberg uncertainty…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…
Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. A pseudospectral method yields a very accurate density of the two-electron ion with nuclear charge close to the critical value.…
Electron charge density is a fundamental physical quantity, determining various properties of matter. In this study, we have proposed a deep-learning model for accurate charge density prediction. Our model naturally preserves physical…
Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement…
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 uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…
Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic indeterminacy in quantum states, Heisenberg's error-disturbance relation (EDR) has been commonly believed as another aspect of the…
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 is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
The strong Scott conjecture about the electron density at a distance 1/Z from an atomic nucleus of charge $Z$ and its generalization for molecules are proved. The density, suitably scaled, converges to an explicit limiting density as $Z \to…
Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
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…
Electronic transport properties for single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions or by means of scanning tunneling…