Impurities in a periodic structure

Frédéric Klopp

Journées équations aux dérivées partielles (1990)

  • page 1-12
  • ISSN: 0752-0360

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Klopp, Frédéric. "Impuretés dans une structure périodique." Journées équations aux dérivées partielles (1990): 1-12. <http://eudml.org/doc/93216>.

@article{Klopp1990,
author = {Klopp, Frédéric},
journal = {Journées équations aux dérivées partielles},
keywords = {Schrödinger operators; semi-classical limit; periodic potentials; spectrum},
language = {fre},
pages = {1-12},
publisher = {Ecole polytechnique},
title = {Impuretés dans une structure périodique},
url = {http://eudml.org/doc/93216},
year = {1990},
}

TY - JOUR
AU - Klopp, Frédéric
TI - Impuretés dans une structure périodique
JO - Journées équations aux dérivées partielles
PY - 1990
PB - Ecole polytechnique
SP - 1
EP - 12
LA - fre
KW - Schrödinger operators; semi-classical limit; periodic potentials; spectrum
UR - http://eudml.org/doc/93216
ER -

References

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  1. [ADH] S. Alama, P. Deift, R. Hempel, Eigenvalue branches of the Schrödinger operator H-λW in a gap of σ(H). Comm. Math. Phys., 121, 1989, 291-321. Zbl0676.47032MR90e:35046
  2. [B] F. Bentosela, Scattering from impurities in a crystal., Comm. Math. Phys. 46, 1976, 153-166. MR52 #14690
  3. [C] J. Callaway, Energy Band Theory., Academic Press, New York/London, 1964. Zbl0121.23303MR28 #5776
  4. [Ca] U. Carlsson, An infinite number of Wells in the semi-classical limit, Preprint de l'université de Lund, 1989 (à paraître dans Asymptotic Analysis). Zbl0727.35094
  5. [DH] P. Deift, R. Hempel, On the existence of eigenvalues of the Schrödinger operator H-λW in a gap of σ(H). Comm. Math. Phys., 103, 1986, 461-490. Zbl0594.34022MR87k:35184
  6. [GS] F. Gesztesy, B. Simon, On a theorem of Deift and Hempel., Comm. Math. Phys. 116, 1988, 503-505. Zbl0647.35063MR89g:35080
  7. [HSj] B. Helffer, J. Sjöstrand, Multiple wells in the semi-classical limit 1, Comm. P.D.E 9 (4) 1984, 337-408. Zbl0546.35053
  8. [KS] M. Klaus, B. Simon, Coupling constant thresholds in non relativistic quantum mechanics., Ann. of Phys. 130, 1980, 251-281. Zbl0455.35112MR82h:81028a
  9. [LL] L. Landau, E. Lifschitz, Mecanique quantique, théorie non relativiste, Editions MIR, Moscou, 1966. Zbl0144.47605
  10. [O] A. Outassourt, Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique, J. Funct. Anal. 72, 1987, 65-93. Zbl0662.35023MR88k:35049
  11. [P] A. Persson, Bounds for the discrete part of the spectrum of a semi-bounded Schrödinger operator, Math. Scand. 8, 1960, 143-153. Zbl0145.14901MR24 #A3412
  12. [S1] B. Simon, Semi-classical analysis of low lying eigenvalues I. Nondegenerate minima: Asymptotic expansion., Annales I.H.P 38 (3), 1983, 295-307. Zbl0526.35027MR85m:81040a
  13. [S2] B. Simon, Semi-classical analysis of low lying eigenvalues III. Width of the ground state band in strongly coupled solids., Ann. of Phys. 158(2), 1984, 415-420. Zbl0596.35028MR87h:81045b
  14. [S3] B. Simon, The bound state of a weakly coupled Schrödinger operator in one or two dimensions., Ann. of Phys. 97, 1976, 279-288. Zbl0325.35029MR53 #8646
  15. [Sk] M.M. Skriganov, Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators., Proc. of the Steklov Inst. of Math., 2, 1987. Zbl0615.47004MR88g:47038

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