Spectrum of semiclassical Schrödinger operators for two-frequency resonance

Article type: Research Article

Authors: Hireche, Faouzi^{a; b} | Ghomari, Kaoutar^{a; b; *}

Affiliations: [a] National Polytechnic School of Oran-Maurice Audin, BP 1523 Oran-El M’naouar, Oran 31000, Algeria. E-mails: faouzi.hireche.ma@gmail.com, faouzienset@gmail.com | [b] Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), Algeria. E-mail: kaoutar.ghomari@enp-oran.dz

Correspondence: [*] Corresponding author. E-mail: kaoutar.ghomari@enp-oran.dz.

Abstract: This article is devoted to an analysis of semiclassical Schrödinger operators for two-frequency resonance of the type 1:p where p is even. The Birkhoff–Gustavson normal form is applied to describe the discrete spectrum in the case where the potential is smooth and admits a nondegenerate global minimum at the origin 0.

Keywords: Birkhoff–Gustavson normal form, Weyl quantization, Schrödinger operator, Harmonic oscillator, Resonance, Bargmann transform

DOI: 10.3233/ASY-211691

Journal: Asymptotic Analysis, vol. 127, no. 1-2, pp. 191-200, 2022