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.
CITATION STYLE
Puertas-Centeno, D., Toranzo, I. V., & Dehesa, J. S. (2018). Exact Rényi entropies of D-dimensional harmonic systems. European Physical Journal: Special Topics, 227(3–4), 345–352. https://doi.org/10.1140/epjst/e2018-00092-4
Mendeley helps you to discover research relevant for your work.