Asymptotic Analysis for Schrödinger Hamiltonians via Birkhoff-Gustavson Normal Form
Résumé
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.
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