Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutators

Abdelwaheb Ifa; Michel Rouleux

doi:10.46298/arima.2593

Abdelwaheb Ifa ; Michel Rouleux - Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutators

arima:2593 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, December 13, 2016, Volume 23 - 2016 - Special issue for LEM2I 2016 - https://doi.org/10.46298/arima.2593

Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutatorsArticle

Authors: Abdelwaheb Ifa ; Michel Rouleux

We revisit in this Note the well known Bohr-Sommerfeld quantization rule (BS) for a 1-D Pseudo-differential self-adjoint Hamiltonian within the algebraic and microlocal framework of Helffer and Sjöstrand; BS holds precisely when the Gram matrix consisting of scalar products of some WKB solutions with respect to the " flux norm " is not invertible.

https://doi.org/10.46298/arima.2593

Source: HAL:hal-01412774v1

Volume: Volume 23 - 2016 - Special issue for LEM2I 2016

Published on: December 13, 2016

Accepted on: December 12, 2016

Submitted on: December 12, 2016

Keywords: Semi-classical spectral asymptotics, quantization rules ,Analyse spectrale semi-classique, règles de quantification,[MATH] Mathematics [math]

Abdelwaheb Ifa ; Michel Rouleux - Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutators

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