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Sur l'équation de Schrödinger avec champ magnétique

Bernard Helffer

Séminaire de théorie spectrale et géométrie (1986-1987)

  • Volume: 5, page 159-164
  • ISSN: 1624-5458

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Helffer, Bernard. "Sur l'équation de Schrödinger avec champ magnétique." Séminaire de théorie spectrale et géométrie 5 (1986-1987): 159-164. <http://eudml.org/doc/114261>.

@article{Helffer1986-1987,
author = {Helffer, Bernard},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {harmonic oscillator; periodic potential},
language = {fre},
pages = {159-164},
publisher = {Institut Fourier},
title = {Sur l'équation de Schrödinger avec champ magnétique},
url = {http://eudml.org/doc/114261},
volume = {5},
year = {1986-1987},
}

TY - JOUR
AU - Helffer, Bernard
TI - Sur l'équation de Schrödinger avec champ magnétique
JO - Séminaire de théorie spectrale et géométrie
PY - 1986-1987
PB - Institut Fourier
VL - 5
SP - 159
EP - 164
LA - fre
KW - harmonic oscillator; periodic potential
UR - http://eudml.org/doc/114261
ER -

References

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  1. [AH-BO] AHARONOV - BOHM. - Significance of Electromagnetic Potentials in the quantum theory, Phys. Rev., vol. 115, 3, 1959. Zbl0099.43102MR110458
  2. [AZ] YA AZBEL. - Energy spectrum of a conduction electron in a magnetic field, Soviet Phys. JETP, vol. 19, 3, 1964. 
  3. [BE-SI] J. BELLISSARD, B. SIMON. - Cantor Spectrum for the Almost Mathieu Equation, J. Funct. Anal., vol. 48, 3, 1982. Zbl0516.47018MR678179
  4. [CA] U. CARLSSON. - Travail en préparation,. 
  5. [HE] B. HELFFER. - Sur l'équation de Schrödinger avec champ magnétique, Exposé n° 10 au Séminaire EDP de l'Ecole polytechnique, 86-87. 
  6. [HE-SJ 1] B. HELFFER, J. SJÖSTRAND . - Multiple wells in the semi-classical limit I, Comm. Partial Differential Equations ,9, 4 ( 1984), 337-408. Zbl0546.35053MR740094
  7. [HE-SJ 2] B. HELFFER, J. SJÖSTRAND. _ Effet tunnel pour l'équation de Schrödinger avec champ magnétique, Preprint de l'Ecole polytechnique, 1986. Zbl0699.35205MR850507
  8. [HE-SJ 3] B. HELFFER, J. SJÖSTRAND. - en préparation,. 
  9. [HE-SJ 4] B. HELFFER, J. SJÖSTRAND. - Analyse semi-classique de l'équation de Harper, Séminaire EDP de l'Ecole polytechnique, exposé 10 , 86-87. Zbl0634.35056
  10. [HE-SJ 5] B. HELFFER, J. SJÖSTRAND. - Proceedings du colloque de St-Jean-de-Monts, Juin , 1987. 
  11. [HO] D. HOFSTADTER. - Energy Levels and Wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B, 1 ( 1976), 2239-2249. 
  12. [LA-O'CA] R. LAVINE ET M. O'CARROLL. - Ground state properties and lower bounds on energy levels of a particle in a uniform magnetic field and external potential, J. Math. Phys., 18 ( 1977), 1908-1912. MR456039
  13. [OU] A. OUTASSOURT. - Analyse semi-classique pour des opérateurs de Schrödinger avec potentiel périodique, J. Funct. Anal., vol. 72, 1, 1987. Zbl0662.35023MR883504
  14. [RE-SI] M. REED, B. SIMON. - Methods of modern Mathematical Physics, Academic Press, 1979. Zbl0405.47007
  15. [SI] B. SIMON. - Semi-classical Analysis of low lying eigenvalues III, Width of the ground state band in strongly coupled solids, Ann Physics, 158 ( 1984), 415-420. Zbl0596.35028MR772619
  16. [WI 1] M. WILKINSON. - Critical properties of electron eigenstates in incommensurate Systems, Proc. Roy. Soc. London Ser. A , 391 ( 1984), 305-350. MR739684
  17. [WI 2] M. WILKINSON. - An example of phase holonomy in WKB theory, J. Phys. A, 17 ( 1984), 3459-3476. MR772333
  18. [WI 3] M. WlLKINSON. - Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field, Proc. Roy. Soc. London Ser. A , 403 ( 1986), 135-166. MR828687
  19. [WI 4] M. WILKINSON. - An exact Effective Hamiltonian for A perturbed Laundau Level, à paraître au J. Phys. A,. Zbl0639.47010MR893109
  20. [WI 5] M. WILKINSON. - An exact renormalisation Group for Bloch Electrons in a Magnetic fields, à paraître au J. Phys. A,. MR914277

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