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Semiclassical analysis of low lying eigenvalues. III: Width of the ground state band in strongly coupled solids. (English) Zbl 0596.35028
[Part I, cf. Ann. Inst. Henri Poincaré, Phys. Théor. 38, 295-308 (1983; Zbl 0526.35027), Corrections ibid. 40, 224 (1984; Zbl 0537.35023).]
Schrödinger operators with periodic potentials in the limit of strong coupling are analyzed. In particular it is shown that the width of the ground state band \(\Delta\) (\(\lambda)\) with coupling constants \(\lambda^ 2\) of the potential behaves like lim -\(\lambda\) \({}^{-1} \log \Delta (\lambda)\). The paper makes heavy use of earlier results of the same author.
Reviewer: H.Siedentop

35J10 Schrödinger operator, Schrödinger equation
82D25 Statistical mechanical studies of crystals
Full Text: DOI
[1] Agmon, S., ()
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[5] \scB. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit, I, Commun. Partial Differential Equations, to appear.
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[10] \scS. R. S. Varadhan, “Large Deviations and Applications,” CBMS Conference Proceedings, to be published by SIAM. · Zbl 0549.60023
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