On generalized Bohr-Sommerfeld quantization rules for operators with PT symmetry

DOI10.1134/S0001434616050060zbMath1348.81277arXiv1601.04923MaRDI QIDQ325517

Abdelwaheb Ifa, Nal M'hadhbi, Michel Rouleux

Publication date: 18 October 2016

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.04923

zbMATH Keywords

Weyl quantizationPT symmetry\(h\)-pseudodifferential operatorBohr-Sommerfeld ruleprincipal symbolquasi-modesub-principal symbol

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Atomic physics (81V45) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Operator algebras with symbol structure (47L15)

Related Items (1)

Non-real eigenvalues for \(\mathcal{PT}\)-symmetric double wells

Cites Work

• Unnamed Item
• Unnamed Item
• Quantization conditions on Riemannian surfaces and the semiclassical spectrum of the Schrödinger operator with complex potential
• The symbol of a function of a pseudodifferential operator
• Berezin-Toeplitz quantization and complex Weyl quantization of the torus \(\mathbb{T}^2\)
• Bohr-Sommerfeld rules to all orders
• Diophantine tori and spectral asymptotics for nonselfadjoint operators
• Exact semiclassical expansions for one-dimensional quantum oscillators
• Quantum normal forms, Moyal star product and Bohr–Sommerfeld approximation
• Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
• Weyl law for semi-classical resonances with randomly perturbed potentials

This page was built for publication: On generalized Bohr-Sommerfeld quantization rules for operators with PT symmetry