Quantization of the classical Lie algorithm in the Bargmann representation

DOI10.1016/0003-4916(91)90034-6zbMath0875.47008OpenAlexW2054276239MaRDI QIDQ1816222

Mirko Degli Esposti, Sandro Graffi, Jan Herczyński

Publication date: 24 November 1996

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0003-4916(91)90034-6

zbMATH Keywords

HamiltonianSchrödinger operatorBargmann representationpolynomial perturbationRayleigh-Schrödinger seriesnon-resonant harmonic oscillators

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Perturbation theories for operators and differential equations in quantum theory (81Q15) General quantum mechanics and problems of quantization (81S99)

Related Items (13)

On the diagonalization of quantum Birkhoff–Gustavson normal form ⋮ Lie-series approach to the evolution of resonant and nonresonant anharmonic oscillators in quantum mechanics ⋮ Diagrams in classical and semiclassical perturbation theory ⋮ On convergence of normal forms for complex frequencies ⋮ Semiclassical estimates for Weyl quantisation ⋮ Rayleigh-Schrödinger series and Birkhoff decomposition ⋮ Time dependent quantum perturbations uniform in the semiclassical regime ⋮ Symbols of operators and quantum evolution ⋮ Normalization in Lie algebras via mould calculus and applications ⋮ A quantum Cherry theorem for perturbations of the plane rotator ⋮ Normalization in Banach scale Lie algebras via mould calculus and applications ⋮ Unnamed Item ⋮ Kato perturbative expansion in classical mechanics and an explicit expression for the Deprit generator

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• Perturbation theory of odd anharmonic oscillators
• An algebra of pseudodifferential operators and the asymptotics of quantum mechanics
• On a Hilbert space of analytic functions and an associated integral transform part I
• Birkhoff-Gustavson normal form in classical and quantum mechanics

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