The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr–Sommerfeld quantization condition, revisited

DOI10.1090/S1061-0022-2011-01183-5zbMath1248.47015arXiv1009.1378MaRDI QIDQ3104497

Dimitri Yafaev

Publication date: 14 December 2011

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1378

zbMATH Keywords

Schrödinger equationpotential wellBohr-Sommerfeld quantization conditionairy functionsGreen-Liouville approximationsemiclassical Weyl formula

Mathematics Subject Classification ID

(2)-body potential quantum scattering theory (81U05) Scattering theory of linear operators (47A40)

Related Items (10)

Molecular predissociation resonances near an energy-level crossing. I: Elliptic interaction ⋮ The geometry of the semiclassical wave front set for Schrödinger eigenfunctions on the torus ⋮ Molecular predissociation resonances near an energy-level crossing. II: Vector field interaction ⋮ Exponential lower resolvent bounds far away from trapped sets ⋮ Eigenvalue spacing for 1D singular Schrödinger operators ⋮ Passage through a potential barrier and multiple wells ⋮ Widths of resonances above an energy-level crossing ⋮ Widths of highly excited resonances in multidimensional molecular predissociation ⋮ Eigenvalue splitting of polynomial order for a system of Schrödinger operators with energy-level crossing ⋮ Semiclassical WKB problem for the non-self-adjoint Dirac operator with a decaying potential

Cites Work

• Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit)
• Semiclassical analysis of low lying eigenvalues. IV. The flea on the elephant
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