The Quantum Mechanics Canonically Associated to Free Probability I: Free Momentum and Associated Kinetic Energy

DOI10.1142/S1230161222500172zbMath1530.81005arXiv2109.10511OpenAlexW4320028513MaRDI QIDQ6157156

Tarek Hamdi, Yun Gang Lu, Luigi Accardi

Publication date: 19 June 2023

Published in: Open Systems & Information Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.10511

zbMATH Keywords

Hilbert transformquantum mechanicsBessel functionsfree probabilitysemi-circle distributionfree kinetic energyfree momentum

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spectrum, resolvent (47A10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Axioms; other general questions in probability (60A05) Bergman spaces and Fock spaces (30H20) Random power series in one complex variable (30B20)

Related Items (1)

The Quantum Mechanics Canonically Associated to Free Probability II: The Normal and Inverse Normal Order Problem

Cites Work

• Quantum probability and spectral analysis of graphs. With a foreword by Professor Luigi Accardi.
• Interacting Fock Spaces and Gaussianization of Probability Measures
• $$*$$ ∗ –Lie Algebras Canonically Associated to Probability Measures on $${\pmb {\varvec{\mathbb {R}}}}$$ R with All Moments
• The Quantum Mechanics Canonically Associated to Free Probability II: The Normal and Inverse Normal Order Problem
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