Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
Archivos
Fecha
2017-04-09
Título de la revista
ISSN de la revista
Título del volumen
Editor
MDPI
Resumen
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 Rényi entropies, respectively, at the limit of large D. The associated multidimensional position-momentum uncertainty relations are discussed, showing that they saturate the corresponding general ones. A conjecture about the Shannon-like uncertainty relation is given, and an interesting phenomenon is observed: the Heisenberg-like and Rényi-entropy-based equality-type uncertainty relations for all of the D-dimensional harmonic oscillator states in the pseudoclassical (D → ∞) limit are the same as the corresponding ones for the hydrogenic systems, despite the so different character of the oscillator and Coulomb potentials.
Descripción
Citación
Entropy 2017, 19, 164
Colecciones
![license logo](./assets/images/cc-licenses/cc-ship.gif)
Excepto si se señala otra cosa, la licencia del ítem se describe como Attribution 4.0 International