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Helffer, B.; Sjöstrand, J.

Analyse semi-classique pour l’équation de Harper. II: Comportement semi-classique près d’un rationnel. (Semiclassical analysis for the Harper equation. II. Semiclassical behaviour near a rational number). (French) Zbl 0714.34131

Mém. Soc. Math. Fr., Nouv. Sér. 40, 139 p. (1990).
[For part I see the paper reviewed in Zbl 0714.34130.]
In this long paper the authors continue their deep study of Harper’s operators in \(L^ 2({\mathbb{R}}): \cos (hD_ x)+\cos x\) by microlocal analysis and renormalisation.
Reviewer: D.Robert

Cited in 2 Reviews
Cited in 39 Documents

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
35P15 Estimates of eigenvalues in context of PDEs
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs

Keywords:

Harper’s operators; microlocal analysis

Citations:

Zbl 0714.34130
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References:

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