A remark on Bohr-Sommerfeld Quantization Rules for a self-adjoint 1-D h-Pseudo-differential operator
Résumé
We revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D $h$-Pseudo-differential
operator 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.
We simplify somewhat our previous proof \cite{IfaLouRo} by working in spatial representation only, as in the complex WKB theory for
Schr\"odinger operator.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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