Quantum Birkhoff-Gustavson normal form in some completely resonant cases

DOI10.1016/J.JMAA.2011.01.004zbMath1208.81079OpenAlexW2069268206MaRDI QIDQ631865

Kaoutar Ghomari, Bekkai Messirdi

Publication date: 14 March 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.01.004

zbMATH Keywords

Birkhoff normal formWeyl quantizationresonancesharmonic oscillator

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Resonance in context of PDEs (35B34)

Related Items (1)

New approach to the procedure of quantum averaging for the Hamiltonian of a resonance harmonic oscillator with polynomial perturbation for the example of the spectral problem for the cylindrical Penning trap

Cites Work

• Wave invariants at elliptic closed geodesics
• Spectral asymptotics via the semiclassical Birkhoff normal form
• The Schrödinger equation and canonical perturbation theory
• Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
• Chaos in classical and quantum mechanics
• Wave-trace invariants
• Resonances of a two-state semiclassical Schrödinger Hamiltonians
• Birkhoff-Gustavson normal form in classical and quantum mechanics
• Resonances of diatomic molecules in the born-oppenheimer approximation
• On the diagonalization of quantum Birkhoff–Gustavson normal form
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