Résonances semi-classiques pour l'opérateur de Schrödinger matriciel en dimension deux
Nedelec, Laurence
Annales de l'I.H.P. Physique théorique, Tome 65 (1996), p. 129-162 / Harvested from Numdam
@article{AIHPA_1996__65_2_129_0,
     author = {Nedelec, Laurence},
     title = {R\'esonances semi-classiques pour l'op\'erateur de Schr\"odinger matriciel en dimension deux},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {65},
     year = {1996},
     pages = {129-162},
     mrnumber = {1411264},
     zbl = {0915.35091},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPA_1996__65_2_129_0}
}
Nedelec, Laurence. Résonances semi-classiques pour l'opérateur de Schrödinger matriciel en dimension deux. Annales de l'I.H.P. Physique théorique, Tome 65 (1996) pp. 129-162. http://gdmltest.u-ga.fr/item/AIHPA_1996__65_2_129_0/

[AC71] J. Aguilar et J.M. Combes, A class of analytic pertubations for one body Schrödinger Hamiltonians, Commun. Math. Phys., Vol. 22, 1971, p. 269-279. | MR 345551 | Zbl 0219.47011

[BCD85] Ph Briet, J.M. Combes et P. Duclos, On the location of resonances for Schrödinger operators in the semiclassical limit I, J. Math. Anal. Appl., Nov. 1985. | Zbl 0629.47043

[BCD87] Ph Briet, J.M. Combes et P. Duclos, On the location of resonances for Schrödinger operators in the semiclassical limit II, Comm. Part. Diff. Eq., Vol. 12, 1987, p. 209-258. | Zbl 0622.47047

[CDS81] J.M. Combes, P. Duclos et R. Seiler, The Born Oppenheimer approximation , Rigorous Atomic and molecular, Physic, 1981, p. 185-212.

[Fed83] M.V. Fedoryuk, Asymptotic analysis, 1983, Springer verlag. | MR 1295032

[GS94] A. Grigis et J. Sjöstrand, Microlocal analysis for diff. op., 1994, Cambridge Univ. Press. | MR 1269107

[Hag90] G.A. Hagedorn, Electron energy level crossing in time dependent Born Oppenheimer approximation, Theoretica Chimica Acta., Vol. 77, 1990, p. 163-190.

[Hag94] G.A. Hagedorn, Molecular propagation through electron energy level crossings, Memoirs A.M.S. 536, Vol. 111, 1994. | MR 1234882 | Zbl 0833.92025

[HeSi81] I. Herbst et B. Simon, Dilation analyticity in constant electric field II. The N-body problem, Borel summability, Commun. Math. Phys., Vol. 80, 1981, p. 181-216. | MR 623157 | Zbl 0473.47038

[HS84] B. Helffer et J. Sjöstrand, Multiple wells in the semi classical limit I, Communication in partial differential equations, Vol. 9 (5), 1984. | Zbl 0546.35053

[HS86] B. Helffer et J. Sjöstrand, Résonances en limite semi-classique, Mémoire de la S.M.F., 1986. | Numdam | Zbl 0631.35075

[HS89] B. Helffer et J. Sjöstrand, Semi classical analysis for Harper's aquation III, Mémoire de la S.M.F., 1989. | Numdam | Zbl 0725.34099

[HS90] B. Helffer et J. Sjöstrand, Analyse semi-classique pour l'équation de Harper II, Mémoire de la S.M.F., Vol. 40,1990. | Numdam | Zbl 0714.34131

[Hun86] W. Hunziker, Distorsion analyticity and molecular resonances curves, Annales de l'I.H.P., mars 1986. | Numdam

[Joy94] A. Joye, Proof of the landau-zener formula, Asympt. Anal., Vol. 9, 1994, p. 209-258. | MR 1295294 | Zbl 0814.35109

[Kat76] Kato, Perturbation theory for linear operators, Springer, 1976. | MR 407617

[Kle87] M. Klein, On the mathematical theory of predissociation, Ann. of Physics, Vol. 178 (1), 1987, p. 48-73. | MR 913151 | Zbl 0649.35024

[KMSW92] M. Klein, A. Martinez, R. Seiler et X.P. Wang, On the Born-Oppenheimer expansion for polyatomic molecules, Comm. Math. Phys., Vol. 143, 1992, p. 607-639. | MR 1145603 | Zbl 0754.35099

[KR93] N. Kaïdi et M. Rouleux, Forme normale d'un hamiltonien à 2 niveaux près d'un point de branchement. Limite semi-classique, C.R.A.S., Vol. 317, série I, 1993, p. 359-364. | MR 1235449 | Zbl 0797.58083

[Lau85] P. Laubin, Hyperbolic boundary value problems..., Proc. Nato asi on adv in Microl. anal., 1985, p. 165-202. | MR 850502

[Mä92] C. März, Spectral asymptotics for Hill's equation near the potential maximum, Asymptotic Analysis, Vol. 5, 1992, p. 221-267. | MR 1145112 | Zbl 0786.34080

[Mar91a] A. Martinez, Résonances dans l'approximation de Born Oppenheimer I, Journal of Differ. Eq., 1991, p. 204-234. | MR 1111174 | Zbl 0737.35046

[Mar91b] A. Martinez, Résonances dans l'approximation de Born Oppenheimer II. Largeur des résonances, Commun. Math. Phys., Vol. 135, 1991, p. 517-530. | MR 1091576 | Zbl 0737.35047

[Mes93] B. Messirdi, Asymptotique de Born-Oppenheimer pour la prédissociation moléculaire (cas des potentiels réguliers), Annales de l'I.H.P., physique théorique, Vol. 61, 1993, p. 255-292. | Numdam | MR 1311068 | Zbl 0812.35109

[Nak94a] S. Nakamura, On an example of phase space tunneling, à paraître, 1994. | Numdam | MR 1357496

[Nak94b] S. Nakamura, Tunneling effects in momentum space and scattering, à paraître, 1994. | MR 1291641 | Zbl 0827.35097

[Pet93] P. Pettersson, W.K.B expansions for systems of Schrödinger operators with crossing eigenvalues, PhD thesis, University of Lund, 1993.

[Sim83] B. Simon, Semi-classical analysis of low lying eigenvalues I. Non degenerate minima : asymptotic expensions, Ann. Inst. Henri Poincaré, Vol. 38, 1983, p. 295-307. | Numdam | MR 708966 | Zbl 0526.35027

[Sj80] J. Sjöstrand, Problèmes aux limites microhyperboliques, Math. Analy., 1980.

[Sj82] J. Sjöstrand, Singularités analytiques microlocales, Vol. 95, Astérisque, 1982. | MR 699623 | Zbl 0524.35007

[SW89] A. Shapere et F. Wilczek, Geometric phases in physics, World Sci., 1989. | MR 1084385