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
NULL##NULL
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.