Semiclassical estimates for Weyl quantisation

DOI10.1006/JFAN.1996.3027zbMath0883.47086OpenAlexW1983211278MaRDI QIDQ1363020

Jan Herczyński

Publication date: 7 August 1997

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1996.3027

zbMATH Keywords

Weyl quantizationposition and momentum operatorsBargmann representationannihilation and creation operatorsHilbert space of holomorphic functionsnonresonant harmonic oscillatorsemiclassical limit of perturbation theory

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Perturbation theories for operators and differential equations in quantum theory (81Q15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Cites Work

• Deformation estimates for the Berezin-Toeplitz quantization
• A note on uniqueness of the normal form for quasi-integrable systems
• The Segal-Bargmann ``coherent state transform for compact Lie groups
• Quantization of the classical Lie algorithm in the Bargmann representation
• Regular and stochastic motion
• On a Hilbert space of analytic functions and an associated integral transform part I
• Approximation of Schrödinger eigenvalues and eigenfunctions by canonical perturbation theory: The periodically driven quantum rotator
• Birkhoff-Gustavson normal form in classical and quantum mechanics
• Nekhoroshev type estimates for quantum propagators
• Time-dependent normal form theory and Schrödinger initial value problems
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