Opérateurs de Schrödinger avec champ magnétique

B. Helffer

Séminaire Équations aux dérivées partielles (Polytechnique) (1986-1987)

  • page 1-14

How to cite


Helffer, B.. "Opérateurs de Schrödinger avec champ magnétique." Séminaire Équations aux dérivées partielles (Polytechnique) (1986-1987): 1-14. <http://eudml.org/doc/111932>.

author = {Helffer, B.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Schrödinger operators; magnetic field; spectral theory; resolvent; first eigenvalue; multiplicity of eigenvalues},
language = {fre},
pages = {1-14},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Opérateurs de Schrödinger avec champ magnétique},
url = {http://eudml.org/doc/111932},
year = {1986-1987},

AU - Helffer, B.
TI - Opérateurs de Schrödinger avec champ magnétique
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1986-1987
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 14
LA - fre
KW - Schrödinger operators; magnetic field; spectral theory; resolvent; first eigenvalue; multiplicity of eigenvalues
UR - http://eudml.org/doc/111932
ER -


  1. [AH-BO] Y. Aharonov - D. Bohm: Significance of Electromagnetic Potentials in the Quantum theoryThe Physical review vol.115 n°3, Aug 1959. Zbl0099.43102MR110458
  2. [AL-BA] S. Alinhac - M.S. Baouendi: Uniqueness for the characteristic cauchy problem and strong unique continuation for higher order partial differential inequalitiesAmer. J. of Math. Vol. 102 n°1 p.179-217. Zbl0425.35098MR556891
  3. [AR] N. Aronszajn: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. (9) 36 (1957) pp.235-249. Zbl0084.30402MR92067
  4. [AV-HE-SI] J. Avron - I. Herbst - B. Simon: Schrödinger operators with magnetic fields: [1] General interactions. Duke Math. Journal Vol.45 n°4 Dec.78 Zbl0399.35029MR518109
  5. [2] Separation of Center of Mass in Homogeneous Magnetic fields.Annals of Physics114 p.431-451 (1978). Zbl0409.35027MR507741
  6. [3] Atoms in Homogeneous Magnetic fieldsComm. Math. Phys.79 p.529-572 (1981). Zbl0464.35086MR623966
  7. [AV-SE] J. Avron - R. Seiler: Paramagnetism for non relativistic Electrons and Euclidian Massless Dirac Particles. Phys. Rev. Letters Vol.42 April 1979 n°15 p.931-934. 
  8. [AV-SI] J.E. Avron - B. Simon: A counter example to the paramagnetic conjecturePhysics letters Vol.75 A n°1,2 (24 Déc. 1979). 
  9. [BE] M. Berry: Journal of Physics serie A (19) (1986) p.2281. Zbl0623.58044MR852496
  10. [C-S-S] J.M. Combes - R. Schrader - R. Seiler: Classical bounds and limits for Energy Distributions of Hamilton operators in Electromagnetic fieldsAnnals of Physics111 p.1-18 (1978). MR489509
  11. [CO] H. Cordes: "Uber die Bestimmtheit der Lösungen elliptischer Differential gleichungen durch Anfangs vorgaben";Nachr. Akad. Wiss.GöttingenII (1956) pp.230-258. Zbl0074.08002
  12. [HA] E.M. Harrell: The band structure of a one dimensional, periodic system in the scaling limit. Ann. Physics119 (1979) p.351-369. Zbl0412.34013MR539149
  13. [HE-MO] B. Helffer - A. Mohamed: Caractérisation du spectre essentiel de l'opérateur de Schrödinger avec un champ magnétique. Manuscrit. Zbl0638.47047
  14. [HE-NO] B. Helffer - J. Nourrigat: Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs. Progress in Mathematics Vol.58, Birkhäuser, Boston (1985). Zbl0568.35003MR897103
  15. [HE-SJ] B. Helffer - J. Sjostrand: [1] Multiple wells in the semi-classical limit I;Comm. in P.D.E.,9 (4) (1984) p.337-408. Zbl0546.35053MR740094
  16. [2] Multiple wells in the semi-classical limit II; Annales de l'I.H.P., vol.42, n°2 (1985) p.127-212. MR798695
  17. [3] Effet tunnel pour l'équation de Schrödinger avec champ magnétique Preprint de l'Ecole Polytechnique Déc.86. 
  18. [HO-SCH-SE] H. Hogreve - R. Schrader - R. Seiler: A conjecture on the spinor functional determinant;Nuclear Phys. B142 (1978) p525. MR509972
  19. [HU] W. Hunziker: Schrödinger Operators with Electric or Magnetic fields Proc. Int. Conf. in Math. Phys., Lausanne (1980) Lect. Notes in Physics n°116. Zbl0471.47010MR582602
  20. [IV] A. Iwatsuka: Magnetic Schrödinger Operators with compact resolventJ. Math. Kyoto Univ.26-3 (1986) p.357-374. Zbl0637.35026MR857223
  21. [JLMS] G. Jona-Lasinio - F. Martinelli et E. Scoppola: New approach in the semi-classical limit of Quantum Mechanics I- Multiple tunneling in one dimension;comm. in Math. Phys.80 (1981) p.223-254. Zbl0483.60094MR623159
  22. [KA] T. Kato: Israël J. of Math.13 (1972) p.125-174. Zbl0246.35025MR333833
  23. [KO] J.J. Kohn: "Lectures on degenerate elliptic problems" CIME1977 p.91-149. Zbl0448.35046MR660652
  24. [LA-LI] Landau - Lifschitz: Mécanique quantique. 
  25. [LA-O'CA] R. Lavine - O'Caroll: Ground state properties and lower bounds of Energy levels of a particle in a uniform magnetic field and external potential;J. of Math. Phys.18 (1977) p.1908-1912. MR456039
  26. [MO] A. Mohamed: Quelques remarques sur le spectre de Schrödinger avec un champ magnétique. Manuscrit. 
  27. [O-P] S. Olariu - I. Iovitzu Popescu: The quantum effects of electromagnetic fluxes;Review of Modern Physics Vol 57 n°2 (1985). 
  28. [OU] A. Outassourt: Effet tunnel pour les opérateurs de Schrödinger à potentiel périodique. Séminaire de l'Université de Nantes (84-85) et à paraître au Journal of Functional Analysis87. 
  29. [PE] M. Peshkin: 1981Phys. Rev. A23360; Aharonov-Bohm effect in Bound states: Theoretical and experimental states. 
  30. [SI] B. Simon: [1]Semi-classical Analysis of low lying Eigenvalues III width of the ground state band in strongly coupled solids. Ann. of Physics158 (1984) p.415-420. Zbl0596.35028MR772619
  31. [2] Semi-classical Analysis of low lying Eigenvalues IV;The flea of the elephant. J. of Functional Analysis Vol.63 n°1 (1985) p.123-136. Zbl0652.35090MR795520
  32. [V-W] C. Von Westenholz: Differential forms in Mathematical Physics; North Holland. Zbl0391.58001MR641034
  33. [WA] X.P. Wang: Effet tunnel pour l'opérateur de Dirac; Ann. I.H.P. Vol.43, n°3 (1985) p.269-319. + Addendum n°4. Zbl0614.35074
  34. [WU-YA] Tai Tsun Wu - Chen Ning Yang: Concept of non integrable factors and global formulation of gauge fields. Phys. Rev. D Vol.12, n°12 Déc.1975. 

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