A remark on Bohr-Sommerfeld Quantization Rules for a self-adjoint 1-D h-Pseudo-differential operator - CNRS - Centre national de la recherche scientifique
Pré-Publication, Document De Travail Année : 2024

A remark on Bohr-Sommerfeld Quantization Rules for a self-adjoint 1-D h-Pseudo-differential operator

Résumé

We revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D $h$-Pseudo-differential operator within the algebraic and microlocal framework of Helffer and Sj\"ostrand; BS holds precisely when the Gram matrix consisting of scalar products of some WKB solutions with respect to the ``flux norm'' is not invertible. We simplify somewhat our previous proof \cite{IfaLouRo} by working in spatial representation only, as in the complex WKB theory for Schr\"odinger operator.
Fichier principal
Vignette du fichier
Michel-Abd.pdf (238.64 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04663314 , version 1 (27-07-2024)

Identifiants

  • HAL Id : hal-04663314 , version 1

Citer

Michel L. Rouleux, Abdelwaheb Ifa. A remark on Bohr-Sommerfeld Quantization Rules for a self-adjoint 1-D h-Pseudo-differential operator. 2024. ⟨hal-04663314⟩
21 Consultations
19 Téléchargements

Partager

More