Quantization conditions on Riemannian surfaces and the semiclassical spectrum of the Schrödinger operator with complex potential

DOI10.1134/S0001434610070205zbMath1234.81077OpenAlexW2078812171WikidataQ115253968 ScholiaQ115253968MaRDI QIDQ650274

A. I. Esina, Andrej I. Shafarevich

Publication date: 25 November 2011

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

Full work available at URL: https://doi.org/10.1134/s0001434610070205

zbMATH Keywords

Schrödinger operatormonodromy matrixturning pointRiemannian surfacequantization conditionholomorphic formsemiclassical spectrum of an operatorStokes line

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (7)

On generalized Bohr-Sommerfeld quantization rules for operators with PT symmetry ⋮ Level lines of harmonic functions related to some Abelian integrals ⋮ Analogs of Bohr-Sommerfeld-Maslov quantization conditions on Riemann surfaces and spectral series of nonself-adjoint operators ⋮ Spectral deformation in a problem of singular perturbation theory ⋮ A quasiclassical limit of the spectrum of a Schrödinger operator with complex periodic potential ⋮ WKB asymptotics and spectral deformation in semi-classical limit ⋮ Asymptotics of the spectrum and eigenfunctions of the magnetic induction operator on a compact two-dimensional surface of revolution

Cites Work

• Quasiclassical spectral asymptotics and the Stokes phenomenon for the Weber equation.
• On the limit behaviour of the spectrum of a model problem for the Orr-Sommerfeld equation with Poiseuille profile
• On perturbation of a multiple eigenvalue
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Quantization conditions on Riemannian surfaces and the semiclassical spectrum of the Schrödinger operator with complex potential