Exact Shannon entropies for the multidimensional harmonic states

2018/10/20 by I. V. Toranzo, J. S. Dehesa · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Curse of dimensionality #Entropic uncertainty #Harmonic #Harmonic oscillator #Mathematical analysis #Mathematics #Monotonic function #Physics #Population #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Statistical physics #Statistics #Uncertainty principle #quant-ph #stochastic dynamics and bifurcation

paper · pdf · doi:10.1016/j.physa.2018.10.026

published as Physica A 516 (2019) 273-279 · Accepted and Published in Physica A

openalex publication_date 2018/10/20 · arxiv created 2018/11/05 · arxiv updated 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this work we determine and discuss the entropic uncertainty measures of Shannon type for all the discrete stationary states of the multidimensional harmonic systems directly in terms of the states' hyperquantum numbers, the dimensionality and the oscillator strength. We have found that these entropies have a monotonically increasing behavior when both the dimensionality and the population of the states are increasing

Citations

• The Shannon-entropy-based uncertainty relation forD-dimensional central potentials
• A Mathematical Theory of Communication
• Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations
• Exact diagonalization of the d-dimensional confined quantum harmonic oscillator
• Entropic properties ofD-dimensional Rydberg systems
• Quantum Computation and Quantum Information

Cited by

• Relative entropic uncertainty relation for scalar quantum fields
• Wehrl entropy, entropic uncertainty relations, and entanglement