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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

##### MSC:
 35J10 Schrödinger operator, Schrödinger equation 82D25 Statistical mechanics of crystals
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##### References:
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