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

Abstract : 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.
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Submitted on : Thursday, December 8, 2016 - 5:38:01 PM
Last modification on : Saturday, June 25, 2022 - 8:32:39 PM
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Abdelwaheb Ifa, Michel L. Rouleux. Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutators. International Conference of the Euro-Maghreb Laboratory of Mathematics and their Interactions LEM2I-2016., Apr 2016, Hammamet, Tunisia. pp.2593, ⟨10.46298/arima.2593⟩. ⟨hal-01314383⟩

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