Asymptotic Analysis for Schrödinger Hamiltonians via Birkhoff-Gustavson Normal Form

Kaoutar Ghomari (1) , Bekkai Messirdi (2) , San Vu Ngoc (3)

1 ENSET d'Oran
2 Université d'Oran
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Fermi resonance; Birkhoff Normal Form; Harmonic oscillator; Bargmann representation; Resonances; Fermi resonance.

Domaines: Physique mathématique [math-ph]

Kaoutar Ghomari, Bekkai Messirdi, San Vu Ngoc. Asymptotic Analysis for Schrödinger Hamiltonians via Birkhoff-Gustavson Normal Form. Asymptotic Analysis, 2013, 85 (1-2), pp.1-28. ⟨10.3233/ASY-131186⟩. ⟨hal-00730276v2⟩