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arXiv · 1605.03759

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

Abdelwaheb Ifa·Michel Rouleux
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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 Sjöstrand; BS holds precisely when the Gram matrix consisting of scalar products of WKB solutions with respect to the "flux norm" is not invertible.

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Abdelwaheb Ifa, Michel Rouleux. 2016-06-20. Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator: The method of positive commutators. https://arxiv.org/abs/1605.03759

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