On the diagonalization of quantum Birkhoff–Gustavson normal form

DOI10.1063/1.531534zbMath0885.47031OpenAlexW2088951014MaRDI QIDQ5284233

A. S. Nikolaev

Publication date: 22 January 1997

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

Full work available at URL: https://doi.org/10.1063/1.531534

zbMATH Keywords

Rayleigh-Schrödinger perturbation expansionquantum Birkhoff-Gustavson normal formVan Vleck perturbation theoryWick normal ordered operators

Mathematics Subject Classification ID

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

Related Items (4)

Kato expansion in quantum canonical perturbation theory ⋮ Quantum Birkhoff-Gustavson normal form in some completely resonant cases ⋮ Manley-Rowe relations for an arbitrary discrete system ⋮ Kato perturbative expansion in classical mechanics and an explicit expression for the Deprit generator

Cites Work

• The Schrödinger equation and canonical perturbation theory
• Quantization of the classical Lie algorithm in the Bargmann representation
• On operators commutative with all invariants for a harmonic oscillator with commensurable frequencies
• The algebraic quantisation of the Birkhoff-Gustavson normal form
• Birkhoff-Gustavson normal form in classical and quantum mechanics
• Improved accuracy of the Birkhoff-Gustavson normal form and its convergence properties
• Canonical transformations depending on a small parameter

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