Spectral asymptotics for Hill's equation near the potential maximum

Christoph März

Journées équations aux dérivées partielles (1990)

  • page 1-10
  • ISSN: 0752-0360

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März, Christoph. "Spectral asymptotics for Hill's equation near the potential maximum." Journées équations aux dérivées partielles (1990): 1-10. <http://eudml.org/doc/93210>.

@article{März1990,
author = {März, Christoph},
journal = {Journées équations aux dérivées partielles},
keywords = {spectrum; semiclassical periodic Schrödinger operator; WKB-form},
language = {eng},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {Spectral asymptotics for Hill's equation near the potential maximum},
url = {http://eudml.org/doc/93210},
year = {1990},
}

TY - JOUR
AU - März, Christoph
TI - Spectral asymptotics for Hill's equation near the potential maximum
JO - Journées équations aux dérivées partielles
PY - 1990
PB - Ecole polytechnique
SP - 1
EP - 10
LA - eng
KW - spectrum; semiclassical periodic Schrödinger operator; WKB-form
UR - http://eudml.org/doc/93210
ER -

References

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  1. [Gé,Gr] C. Gérard, A. Grigis : Precise Estimates of Tunneling and Eigenvalues near a Potential Barrier ; J. of Diff. Eq. 72, 149-177 (1988). Zbl0668.34022MR89h:34024
  2. [Ha] E.M. Harrell : The Band Structure of a One-dimensional Periodic System in a Scaling Limit; Ann. Physics 119, 351-369 (1979) Zbl0412.34013MR80i:34031
  3. [He,Sj 1] B. Helffer, J. Sjöstrand : Multiple Wells in the Semiclassical Limit I, Comm. PDE, 9(4), 337-408 (1984) Zbl0546.35053MR86c:35113
  4. [He,Sj 2] B. Helffer, J. Sjöstrand : Semiclassical Analysis of Harper's Equation III ; Bull. de la S.M.F., Mémoire, to appear (1990) Zbl0759.47022
  5. [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) 
  6. [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) Zbl0194.12202MR41 #5719
  7. [Mz] C. März : Spectral Asymptotics for Hill's Equation near the Potential Maximum ; Thesis, Université de Paris Sud, (April 1990) 
  8. [Ou] A. Outassourt : Comportement Semi-classique pour l'Opérateur de Schrödinger à Potentiel Périodique ; J. of Funct. Anal. 72, 65-93 (1987) Zbl0662.35023MR88k:35049
  9. [Re,Si] M. Reed, B. Simon : Methods of Modern Mathematical Physics IV ; Academic Press (1978) Zbl0401.47001MR58 #12429c
  10. [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) Zbl0596.35028MR87h:81045b
  11. [Sj 1] J. Sjöstrand : Singularités analytiques microlocales ; Astérisque N° 95 (1982) Zbl0524.35007MR84m:58151
  12. [Sj 2] J. Sjöstrand : Density of States Oscillations for Magnetic Schrödinger Operators ; Preprint (1990) 
  13. [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)) Zbl0615.47004MR88g:47038
  14. [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) Zbl0652.34033MR88j:34056

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