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Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator: The method of positive commutators (1605.03759v2)
Published 12 May 2016 in math-ph and 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.