Bohr-Sommerfeld quantization rules revisited : The method of positive commutators 利用統計を見る

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アイテムタイプ	紀要論文 / Departmental Bulletin Paper
言語	英語
キーワード	Bohr Sommerfeld, Weyl quantization, positive commutators, flux norm, microlocal Wronskian
著者	Ifa Abdelwaheb Louati Hanen Rouleux Michel
著者所属	Université de Tunis El-Manar, Département de Mathématiques Université de Tunis El-Manar, Département de Mathématiques／Aix Marseille Univ., Univ. Toulon, CNRS, CPT Aix Marseille Univ., Univ. Toulon, CNRS, CPT
抄録	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. It is simplified by using action-angle variables. The interest of this procedure lies in its possible generalization to matrix-valued Hamiltonians, like Bogoliubov-de Gennes Hamiltonian.
雑誌名	Journal of Mathematical Sciences The University of Tokyo
巻	25
号	2
ページ	91 - 127
発行年	2018-06-29
ISSN	13405705
書誌レコードID	AA11021653
Mathmatical Subject Classification	81S10(MSC2010) 81S30(MSC2010)
出版者	Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日	2017-04-04

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