Suchergebnisse

Agencia Andaluza del Conocimiento of the Junta de Andalucia (Spain), Grant/Award Number: PY20-00082; European Regional Development Fund (FEDER), Grant/Award Number: PID2020-113390GB-I00; Agencia Estatal de Investigacion (Spain), Grant/Award Number: FIS2017-89349P; Basque Government and UPV/EHU, Grant/Award Number: IT1249-19 ; The Jacobi polynomials Poa,ss THORN n oxTHORN conform the canonical family of hypergeometric orthogonal polynomials (HOPs) with the two-parameter weight function o1 xTHORNao1thornxTHORN ss, a,ss > 1, on the interval 1/21, thorn1. The spreading of its associated probability density (i.e., the Rakhmanov density) over the support interval has been quantified, beyond the dispersion measures (moments around the origin, variance), by the algebraic Lq-norms (Shannon and Renyi entropies) and the monotonic complexity-like measures of Cramer-Rao, Fisher-Shannon, and LMC (LopezRuiz, Mancini, and Calbet) types. These quantities, however, have been often determined in an analytically highbrow, non-handy way; specially when the degree or the parameters oa, ss THORN are large. In this work, we determine in a simple, compact form the leading term of the entropic and complexity-like properties of the Jacobi polynomials in the two extreme situations: (n!8; fixed a, ss) and (a!8; fixed n, ss). These two asymptotics are relevant per se and because they control the physical entropy and complexity measures of the high energy (Rydberg) and high dimensional (pseudoclassical) states of many exactly, conditional exactly, and quasi-exactly solvable quantum- mechanical potentials which model numerous atomic and molecular systems. ; Junta de Andalucia PY20-00082 ; European Commission PID2020-113390GB-I00 ; Agencia Estatal de Investigacion (Spain) FIS2017-89349P ; Basque Government IT1249-19 ; UPV/EHU IT1249-19

In this work, the one-parameter Fisher–Rényi measure of complexity for general d-dimensional probability distributions is introduced and its main analytic properties are discussed. Then, this quantity is determined for the hydrogenic systems in terms of the quantum numbers of the quantum states and the nuclear charge. ; This work was partially supported by the Projects P11-FQM-7276 and FQM-207 of the Junta de Andalucia, and by the MINECO (Ministerio de Economía y Competitividad) and FEDER (European regional development fund) grants FIS2014- 54497P and FIS2014-59311P. Ł.R. acknowledges financial support by the grant number 2014/13/D/ST2/01886 of the National Science Center, Warsaw, Poland. Research in Cologne is supported by the Excellence Initiative of the German Federal and State Governments (Grant ZUK 81) and the DFG (GRO 4334/2-1). Ł.R. also acknowledges the support by the Foundation for Polish Science (FNP) and hospitality of the Freiburg Center for Data Analysis and Modeling. I.V.T. acknowledges the support of the Spanish Ministerio de Educación under the program FPU 2014.