Eur. Phys. J. Special Topics 227, 345–352 (2018)
https://doi.org/10.1140/epjst/e2018-00092-4

Regular Article

Exact Rényi entropies of D-dimensional harmonic systems

¹ Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, Granada 18071, Spain
² Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain

^a e-mail: ivtoranzo@ugr.es

Received: 12 October 2017
Received in final form: 15 December 2017
Published online: 28 September 2018

Abstract

The determination of the uncertainty measures of multidimensional quantum systems is a relevant issue per se and because these measures, which are functionals of the single-particle probability density of the systems, describe numerous fundamental and experimentally accessible physical quantities. However, it is a formidable task (not yet solved, except possibly for the ground and a few lowest-lying energetic states) even for the small bunch of elementary quantum potentials which are used to approximate the mean-field potential of the physical systems. Recently, the dominant term of the Heisenberg and Rényi measures of the multidimensional harmonic system (i.e., a particle moving under the action of a D-dimensional quadratic potential, D > 1) has been analytically calculated in the high-energy (i.e., Rydberg) and the high-dimensional (i.e., pseudoclassical) limits. In this work we determine the exact values of the Rényi uncertainty measures of the D-dimensional harmonic system for all ground and excited quantum states directly in terms of D, the potential strength and the hyperquantum numbers.