Fourier transforms, fractional derivatives, and a little bit of quantum mechanics

DOI10.1216/rmj.2020.50.415zbMath1479.46053arXiv1912.01836OpenAlexW3030709289MaRDI QIDQ2188436

Fabio Bagarello

Publication date: 11 June 2020

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.01836

zbMATH Keywords

Fourier transformsfractional derivativesfractional momentum operator

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Fractional derivatives and integrals (26A33) Applications of functional analysis in quantum physics (46N50)

Cites Work

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• \(kq\)-representation for pseudo-bosons, and completeness of bi-coherent states
• Computation of fractional derivatives using Fourier transform and digital FIR differentiator.
• Non-Selfadjoint Operators in Quantum Physics
• Generalized delta functions and their use in quantum optics
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Coordinate representation for non-Hermitian position and momentum operators
• Fractional Quantum Mechanics

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