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Article type: Research Article
Authors: Ghomari, Kaoutar; | Messirdi, Bekkai | Vũ Ngọc, San
Affiliations: Department of Mathematics and Computer Sciences, ENP-Oran, El'Mnaouar, Algeria. E-mails: kaoutar.ghomari@gmail.com, ghomari_kaoutar@yahoo.fr | Department of Mathematics, University of Oran Es-Senia, El'Mnaouar, Algeria. E-mail: messirdi.bekkai@univ-oran.dz | Mathematics Research Institute IRMAR, University of Rennes 1 and Institut Universitaire de France, Rennes, France. E-mail: san.vu-ngoc@univ-rennes1.fr
Note: [] Corresponding author: Kaoutar Ghomari, Department of Mathematics and Computer Sciences, ENP-Oran, BP 1523 El'Mnaouar 31000, Algeria. E-mail: ghomari_kaoutar@yahoo.fr
Abstract: This article reviews the Birkhoff–Gustavson normal form theorem (BGNF) near an equilibrium point of a quantum Hamiltonian. The BGNF process is thereafter used to investigate the spectrum of Schrödinger operators in the 1:1, 1:2 and 1:3 resonances. A computer program is proposed to compute the coefficients of the BGNF up to any order.
Keywords: Birkhoff normal form, harmonic oscillator, Bargmann representation, resonances, Fermi resonance
DOI: 10.3233/ASY-131186
Journal: Asymptotic Analysis, vol. 85, no. 1-2, pp. 1-28, 2013
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