Semiclassical analysis of low lying eigenvalues. III: Width of the ground state band in strongly coupled solids. (English) Zbl 0596.35028

Simon, Barry

Ann. Phys. 158, 415-420 (1984).

[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

Keywords:

leading asymptotics; double wells; Schrödinger operators with periodic potentials; strong coupling; ground state band

Citations:

Zbl 0526.35027; Zbl 0537.35023

References:

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[5]	{\scB. Helffer and J. Sjöstrand}, Multiple wells in the semi-classical limit, I, Commun. Partial Differential Equations, to appear.
[6]	{\scJ. Keller and M. Weinstein}, in preparation.
[7]	Reed, M.; Simon, B., (), “Analysis of Operators” · Zbl 0517.47006
[8]	Simon, B., Ann. inst. Henri Poincaré, 38, 295-307, (1983)
[9]	Simon, B., Ann. of math., 120, 89-118, (1984)
[10]	{\scS. R. S. Varadhan}, “Large Deviations and Applications,” CBMS Conference Proceedings, to be published by SIAM. · Zbl 0549.60023