A. Ifa, N. M'Hadbi, M. Rouleux, “On Generalized Bohr–Sommerfeld Quantization Rules for Operators with PT Symmetry”, Mat. Zametki, 2016, Volume 99, Issue 5,Pages <nobr>673

On Generalized Bohr–Sommerfeld Quantization Rules for Operators with PT Symmetry

A. Ifa^a, N. M'Hadbi^ab, M. Rouleux^cde

^a University of Tunis El Manar
^b King Abdulaziz University
^c Aix-Marseille Université
^d Université de Toulon
^e CNRS – Center of Theoretical Physics

Abstract: We give Bohr–Sommerfeld rules corresponding to quasi-eigenvalues in the pseudospectrum for a one-dimensional $h$-pseudodifferential operator verifying PT symmetry.

Keywords: Bohr–Sommerfeld rule, $h$-pseudodifferential operator, PT symmetry, principal symbol, sub-principal symbol, Weyl quantization, quasi-mode.

UDC: 517

Received: 01.09.2015

DOI: 10.4213/mzm11106