Asymptotic analysis for Schrodinger Hamiltonians via Birkhoff-Gustavson normal form

作者：Ghomari Kaoutar^*; Messirdi Bekkai; Ngoc San Vu

来源：Asymptotic Analysis, 2013, 85(1-2): 1-28.

DOI：10.3233/ASY-131186

• Birkhoff normal form
• harmonic oscillator
• Bargmann representation
• resonances
• Fermi resonance

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 Schrodinger 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.

• 出版日期2013