Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems

Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems

The D-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work, we rigorously determine the leading term of the Heisenberg-like and entropy-like uncertainty measures of this system as given by the radial expectation values and the Ré...

Entropic uncertainty measures for large dimensional hydrogenic systems

An Infinite - Dimensional Heisenberg Uncertainty Principle

An analogue of the classical Heisenberg inequality is given for an infinite-dimensional space. The proof relies on a commutation relationship and integration by parts formula for Gaussian measure. We also discuss when the equality holds.

Heisenberg uncertainty relation and statistical measures in the square well

A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisenberg uncertainty relation, ∆x∆p. It is observed that the extreme values of ∆x...

Entropic bounds on semiclassical measures for quantized one-dimensional maps

Quantum ergodicity asserts that almost all infinite sequences of eigenstates of a quantized ergodic system are equidistributed in the phase space. On the other hand, there are might exist exceptional sequences which converge to different (non-Liouville) classical invariant measures μ. By the remarkable result of N. Anantharaman and S. Nonnenmacher math-ph/0610019, arXiv:0704.1564 (with H. Koch)...