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The European Physical Journal Special Topics

, Volume 227, Issue 3–4, pp 345–352 | Cite as

Exact Rényi entropies of D-dimensional harmonic systems

  • David Puertas-Centeno
  • Irene Valero ToranzoEmail author
  • Jesús Sánchez Dehesa
Regular Article
Part of the following topical collections:
  1. Quantum Systems In and Out of Equilibrium - Fundamentals, Dynamics and Applications

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.

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Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • David Puertas-Centeno
    • 1
    • 2
  • Irene Valero Toranzo
    • 1
    • 2
    Email author
  • Jesús Sánchez Dehesa
    • 1
    • 2
  1. 1.Departamento de Física Atómica, Molecular y Nuclear, Universidad de GranadaGranadaSpain
  2. 2.Instituto Carlos I de Física Teórica y Computacional, Universidad de GranadaGranadaSpain

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