@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}, pages = {129--162}, publisher = {Gauthier-Villars}, volume = {65}, number = {2}, year = {1996}, mrnumber = {1411264}, zbl = {0915.35091}, language = {fr}, url = {http://archive.numdam.org/item/AIHPA_1996__65_2_129_0/} }
TY - JOUR AU - Nedelec, Laurence TI - Résonances semi-classiques pour l'opérateur de Schrödinger matriciel en dimension deux JO - Annales de l'I.H.P. Physique théorique PY - 1996 SP - 129 EP - 162 VL - 65 IS - 2 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1996__65_2_129_0/ LA - fr ID - AIHPA_1996__65_2_129_0 ER -
%0 Journal Article %A Nedelec, Laurence %T Résonances semi-classiques pour l'opérateur de Schrödinger matriciel en dimension deux %J Annales de l'I.H.P. Physique théorique %D 1996 %P 129-162 %V 65 %N 2 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1996__65_2_129_0/ %G fr %F 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, Volume 65 (1996) no. 2, pp. 129-162. http://archive.numdam.org/item/AIHPA_1996__65_2_129_0/
[AC71] A class of analytic pertubations for one body Schrödinger Hamiltonians, Commun. Math. Phys., Vol. 22, 1971, p. 269-279. | MR | Zbl
et ,[BCD85] On the location of resonances for Schrödinger operators in the semiclassical limit I, J. Math. Anal. Appl., Nov. 1985. | Zbl
, et ,[BCD87] On the location of resonances for Schrödinger operators in the semiclassical limit II, Comm. Part. Diff. Eq., Vol. 12, 1987, p. 209-258. | Zbl
, et ,[CDS81] The Born Oppenheimer approximation , Rigorous Atomic and molecular, Physic, 1981, p. 185-212.
, et ,[Fed83] Asymptotic analysis, 1983, Springer verlag. | MR
,[GS94] Microlocal analysis for diff. op., 1994, Cambridge Univ. Press. | MR
et ,[Hag90] Electron energy level crossing in time dependent Born Oppenheimer approximation, Theoretica Chimica Acta., Vol. 77, 1990, p. 163-190.
,[Hag94] Molecular propagation through electron energy level crossings, Memoirs A.M.S. 536, Vol. 111, 1994. | MR | Zbl
,[HeSi81] Dilation analyticity in constant electric field II. The N-body problem, Borel summability, Commun. Math. Phys., Vol. 80, 1981, p. 181-216. | MR | Zbl
et ,[HS84] Multiple wells in the semi classical limit I, Communication in partial differential equations, Vol. 9 (5), 1984. | Zbl
et ,[HS86] Résonances en limite semi-classique, Mémoire de la S.M.F., 1986. | Numdam | Zbl
et ,[HS89] Semi classical analysis for Harper's aquation III, Mémoire de la S.M.F., 1989. | Numdam | Zbl
et ,[HS90] Analyse semi-classique pour l'équation de Harper II, Mémoire de la S.M.F., Vol. 40,1990. | Numdam | Zbl
et ,[Hun86] Distorsion analyticity and molecular resonances curves, Annales de l'I.H.P., mars 1986. | Numdam
,[Joy94] Proof of the landau-zener formula, Asympt. Anal., Vol. 9, 1994, p. 209-258. | MR | Zbl
,[Kat76] Perturbation theory for linear operators, Springer, 1976. | MR
,[Kle87] On the mathematical theory of predissociation, Ann. of Physics, Vol. 178 (1), 1987, p. 48-73. | MR | Zbl
,[KMSW92] On the Born-Oppenheimer expansion for polyatomic molecules, Comm. Math. Phys., Vol. 143, 1992, p. 607-639. | MR | Zbl
, , et ,[KR93] 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 | Zbl
et ,[Lau85] Hyperbolic boundary value problems..., Proc. Nato asi on adv in Microl. anal., 1985, p. 165-202. | MR
,[Mä92] Spectral asymptotics for Hill's equation near the potential maximum, Asymptotic Analysis, Vol. 5, 1992, p. 221-267. | MR | Zbl
,[Mar91a] Résonances dans l'approximation de Born Oppenheimer I, Journal of Differ. Eq., 1991, p. 204-234. | MR | Zbl
,[Mar91b] Résonances dans l'approximation de Born Oppenheimer II. Largeur des résonances, Commun. Math. Phys., Vol. 135, 1991, p. 517-530. | MR | Zbl
,[Mes93] 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 | Zbl
,[Nak94a] On an example of phase space tunneling, à paraître, 1994. | Numdam | MR
,[Nak94b] Tunneling effects in momentum space and scattering, à paraître, 1994. | MR | Zbl
,[Pet93] W.K.B expansions for systems of Schrödinger operators with crossing eigenvalues, PhD thesis, University of Lund, 1993.
,[Sim83] 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 | Zbl
,[Sj80] Problèmes aux limites microhyperboliques, Math. Analy., 1980.
,[Sj82] Singularités analytiques microlocales, Vol. 95, Astérisque, 1982. | Numdam | MR | Zbl
,[SW89] Geometric phases in physics, World Sci., 1989. | MR
et ,