Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator: The method of positive commutators
Mathematical Physics
2016-06-21 v2 math.MP
Abstract
We revisit in this Note the well known Bohr-Sommerfeld quantization rule (BS) for 1-D Pseudo-differential self-adjoint Hamiltonians within the algebraic and microlocal framework of Helffer and Sj\"ostrand; BS holds precisely when the Gram matrix consisting of scalar products of WKB solutions with respect to the "flux norm" is not invertible.
Keywords
Cite
@article{arxiv.1605.03759,
title = {Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator: The method of positive commutators},
author = {Abdelwaheb Ifa and Michel Rouleux},
journal= {arXiv preprint arXiv:1605.03759},
year = {2016}
}