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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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[1] Agmon, S., (Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations. Bounds on Eignefunctions of \(N\)-Body Schrodinger Operators. Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations. Bounds on Eignefunctions of \(N\)-Body Schrodinger Operators, Mathematical Notes (1982), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J) · Zbl 0503.35001
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