2016/07/04 by I. V. Toranzo, David Puertas‐Centeno, D. Puertas-Centeno +1 · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Density functional theory #Excited state #Graphane #Ionization #Laguerre polynomials #Mathematical physics #Mathematics #Orthonormal basis #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Rydberg formula #Statistical Mechanics and Entropy #Wave function #quant-ph
paper · pdf · doi:10.1016/j.physa.2016.06.144
published as Physica A 462 (2016) 1197-1206
openalex publication_date 2016/07/04 · openalex created_date 2016/07/22 · arxiv created 2016/09/05 · arxiv updated 2016/10/07 · openalex updated_date 2026/08/05
The fundamental information-theoretic measures (the Rényi Rp[ρ] and Tsallis Tp[ρ] entropies, p>0) of the highly-excited (Rydberg) quantum states of the D-dimensional (D>1) hydrogenic systems, which include the Shannon entropy (p → 1) and the disequilibrium (p = 2), are analytically determined by use of the strong asymptotics of the Laguerre orthogonal polynomials which control the wavefunctions of these states. We first realize that these quantities are derived from the entropic moments of the quantum-mechanical probability ρ(r) densities associated to the Rydberg hydrogenic wavefunctions Ψ_n,l,\μ\(r), which are closely connected to the \mathfrakLp-norms of the associated Laguerre polynomials. Then, we determine the (n→∞)-asymptotics of these norms in terms of the basic parameters of our system (the dimensionality D, the nuclear charge and the hyperquantum numbers (n,l,\μ\) of the state) by use of recent techniques of approximation theory. Finally, these three entropic quantities are analytically and numerically discussed in terms of the basic parameters of the system for various particular states.