Simon, Barry Semiclassical analysis of low lying eigenvalues. III: Width of the ground state band in strongly coupled solids. (English) Zbl 0596.35028 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 Cited in 1 ReviewCited in 33 Documents 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 PDFBibTeX XMLCite \textit{B. Simon}, Ann. Phys. 158, 415--420 (1984; Zbl 0596.35028) Full Text: DOI References: [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 [2] Carmona, R.; Simon, B., Cummun. Math. Phys., 80, 59-98 (1981) [3] Harrel, E., Commun. Math. Phys., 60, 73-95 (1978) [4] Harrell, E., Ann. Phys. (NY), 119, 351-369 (1979) [5] B. Helffer and J. SjöstrandCommun. Partial Differential Equations; B. Helffer and J. SjöstrandCommun. Partial Differential Equations [6] J. Keller and M. Weinstein; J. Keller and M. Weinstein [7] Reed, M.; Simon, B., (Methods of Modern Mathematical Physics, Vol. IV (1977), Academic Press: Academic Press New York), “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] S. R. S. Varadhan; S. R. S. Varadhan · Zbl 0549.60023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.