Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems

作者：Puertas Centeno David; Toranzo Irene V; Dehesa Jesus S

来源：Entropy, 2017, 19(4): 164.

DOI：10.3390/e19040164

• entropic uncertainty measures
• D-dimensional harmonic oscillator
• D-dimensional quantum physics
• radial and momentum expectation values
• harmonic states at large dimensions

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 Renyi 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 Renyi-entropy-based equality-type uncertainty relations for all of the D-dimensional harmonic oscillator states in the pseudoclassical (D -> infinity) limit are the same as the corresponding ones for the hydrogenic systems, despite the so different character of the oscillator and Coulomb potentials.

• 出版日期2017-4