Spectral asymptotics for Hill's equation near the potential maximum
Journées équations aux dérivées partielles (1990), article no. 15, 10 p. 
@article{JEDP_1990____A15_0,
     author = {M\"arz, Christoph},
     title = {Spectral asymptotics for {Hill's} equation near the potential maximum},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {15},
     pages = {1--10},
     publisher = {Ecole polytechnique},
     year = {1990},
     zbl = {0707.34049},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1990____A15_0/}
}
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März, Christoph. Spectral asymptotics for Hill's equation near the potential maximum. Journées équations aux dérivées partielles (1990), article  no. 15, 10 p. http://www.numdam.org/item/JEDP_1990____A15_0/

[Gé,Gr] C. Gérard, A. Grigis : Precise Estimates of Tunneling and Eigenvalues near a Potential Barrier ; J. of Diff. Eq. 72, 149-177 (1988). | MR | Zbl

[Ha] E.M. Harrell : The Band Structure of a One-dimensional Periodic System in a Scaling Limit; Ann. Physics 119, 351-369 (1979) | MR | Zbl

[He,Sj 1] B. Helffer, J. Sjöstrand : Multiple Wells in the Semiclassical Limit I, Comm. PDE, 9(4), 337-408 (1984) | MR | Zbl

[He,Sj 2] B. Helffer, J. Sjöstrand : Semiclassical Analysis of Harper's Equation III ; Bull. de la S.M.F., Mémoire, to appear (1990) | Numdam

[Hor] W. Horn : Semiclassical Approximation for Tunneling near the Top of a Potential Barrier and its Applications to Solid State Physics ; Thesis, Univ. of California, Los Angeles (1989)

[Ly,Ke] R. Lynn, J.B. Keller : Uniform Asymptotic Solutions of Second Order Linear Ordinary Differential Equations with Turning Points ; Comm. Pure Appl. Math. 23, 379-408 (1970) | MR | Zbl

[Mz] C. März : Spectral Asymptotics for Hill's Equation near the Potential Maximum ; Thesis, Université de Paris Sud, (April 1990)

[Ou] A. Outassourt : Comportement Semi-classique pour l'Opérateur de Schrödinger à Potentiel Périodique ; J. of Funct. Anal. 72, 65-93 (1987) | MR | Zbl

[Re,Si] M. Reed, B. Simon : Methods of Modern Mathematical Physics IV ; Academic Press (1978) | MR | Zbl

[Si] B. Simon : Semiclassical Analysis of Low Lying Eigenvalues III : Width of the Ground State Band in Strongly Coupled Solids ; Ann. Physics 158, 415-420 (1984) | MR | Zbl

[Sj 1] J. Sjöstrand : Singularités analytiques microlocales ; Astérisque N° 95 (1982) | Numdam | MR | Zbl

[Sj 2] J. Sjöstrand : Density of States Oscillations for Magnetic Schrödinger Operators ; Preprint (1990)

[Sk] M.M. Skriganov : Geometric and Arithmethic Methods in the Spectral Theory of Multidimensional Periodic Operators ; Proc. of the Steklov Inst. of Math. 171 (1987 (2)) | MR | Zbl

[We,Ke] M.I. Weinstein, J.B. Keller : Asymptotic Behavior of Stability Regions for Hill's Equation ; SIAM J. Appl. Math. 47(5), 941-958 (1987) | MR | Zbl