Bohr-Sommerfeld quantization rules revisited: the method of positive commutators
Mathematical Physics
2018-04-02 v3 math.MP
Abstract
We revisit 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 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. The interest of this procedure lies in its possible generalization to matrix-valued Hamiltonians, like Bogoliubov-de Gennes Hamiltonian. It is simplified in the scalar case by using action-angle variables.
Keywords
Cite
@article{arxiv.1702.06758,
title = {Bohr-Sommerfeld quantization rules revisited: the method of positive commutators},
author = {Abdelwaheb Ifa and Hanen Louati and Michel Rouleux},
journal= {arXiv preprint arXiv:1702.06758},
year = {2018}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1605.03759