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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 3, Pages 487–506
DOI: https://doi.org/10.4213/tmf6411 (Mi tmf6411) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Quantum Birkhoff normal forms

A. Yu. Anikin

N. E. Bauman Moscow State Technical University, Moscow, Russia
Full-text PDF (510 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf6411
Abstract: We consider quantum analogues of several theorems on Birkhoff normal forms and prove a quantum analogue of the theorem on reducing a Hamiltonian to the normal form and the analogue of the theorem on reducing a Hamiltonian to the real normal form. We obtain the normal form explicitly in the nonresonant case. We consider the uniqueness problems of the normal form and of the normalizing transformation in the nonresonant and resonant cases.
Keywords: Birkhoff normal form, quantum analogue, algebra of observables, automorphism.
Received: 15.10.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 3, Pages 1274–1291
DOI: https://doi.org/10.1007/s11232-009-0115-2
Bibliographic databases:
Language: Russian
Citation: A. Yu. Anikin, “Quantum Birkhoff normal forms”, TMF, 160:3 (2009), 487–506; Theoret. and Math. Phys., 160:3 (2009), 1274–1291
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6411
  • https://doi.org/10.4213/tmf6411
  • https://www.mathnet.ru/eng/tmf/v160/i3/p487
    • This publication is cited in the following 5 articles:
    1. E. M. Novikova, “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”, Math. Notes, 109:5 (2021), 777–793  mathnet  crossref  crossref  isi  elib
    2. Novikova E.M., “On Calculating the Coefficients in the Quantum Averaging Procedure For the Hamiltonian of the Resonance Harmonic Oscillator Perturbed By a Differential Operator With Polynomial Coefficients”, Russ. J. Math. Phys., 28:3 (2021), 406–410  crossref  mathscinet  isi
    3. E. M. Novikova, “Algebra of Symmetries of Three-Frequency Hyperbolic Resonance”, Math. Notes, 106:6 (2019), 940–956  mathnet  mathnet  crossref  isi  scopus
    4. Anikin A., “Non-commutative normal form, spectrum and inverse problem”, Asymptotic Anal., 101:4 (2017), 207–225  crossref  mathscinet  zmath  isi  scopus
    5. Novikova, EM, “Minimal basis of the symmetry algebra for three-frequency resonance”, Russian Journal of Mathematical Physics, 16:4 (2009), 518  crossref  mathscinet  zmath  adsnasa  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:622
    Full-text PDF :275
    References:85
    First page:13
     
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