Théorie de la diffusion pour l'équation de Schrödinger
Séminaire Bourbaki : vol. 1978/79, exposés 525-542, Séminaire Bourbaki, no. 21 (1980), Exposé no. 533, 19 p.
@incollection{SB_1978-1979__21__132_0,
     author = {Cartier, Pierre},
     title = {Th\'eorie de la diffusion pour l'\'equation de {Schr\"odinger}},
     booktitle = {S\'eminaire Bourbaki : vol. 1978/79, expos\'es 525-542},
     series = {S\'eminaire Bourbaki},
     note = {talk:533},
     pages = {132--150},
     publisher = {Springer-Verlag},
     number = {21},
     year = {1980},
     mrnumber = {572422},
     zbl = {0435.35027},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1978-1979__21__132_0/}
}
TY  - CHAP
AU  - Cartier, Pierre
TI  - Théorie de la diffusion pour l'équation de Schrödinger
BT  - Séminaire Bourbaki : vol. 1978/79, exposés 525-542
AU  - Collectif
T3  - Séminaire Bourbaki
N1  - talk:533
PY  - 1980
SP  - 132
EP  - 150
IS  - 21
PB  - Springer-Verlag
UR  - http://archive.numdam.org/item/SB_1978-1979__21__132_0/
LA  - fr
ID  - SB_1978-1979__21__132_0
ER  - 
%0 Book Section
%A Cartier, Pierre
%T Théorie de la diffusion pour l'équation de Schrödinger
%B Séminaire Bourbaki : vol. 1978/79, exposés 525-542
%A Collectif
%S Séminaire Bourbaki
%Z talk:533
%D 1980
%P 132-150
%N 21
%I Springer-Verlag
%U http://archive.numdam.org/item/SB_1978-1979__21__132_0/
%G fr
%F SB_1978-1979__21__132_0
Cartier, Pierre. Théorie de la diffusion pour l'équation de Schrödinger, dans Séminaire Bourbaki : vol. 1978/79, exposés 525-542, Séminaire Bourbaki, no. 21 (1980), Exposé no. 533, 19 p. http://archive.numdam.org/item/SB_1978-1979__21__132_0/

[1] V. De Alfaro et T. Regge - Potential scattering , North Holland , Amsterdam , 1965. | Zbl

[2] W. Amrein , J. Jauch , K. Sinha - Scattering theory in quantum mechanics , Benjamin, New York , 1977 . | MR | Zbl

[3] K.O. Friedrichs - Perturbation of spectra in Hilbert space , Amer. Math. Soc. Lect. in Appl. Math. , vol. 3 , Providence , 1965 . | MR | Zbl

[4] T. Kato - Perturbation theory for linear operators , 2e édit. , Springer , New York, 1976 . | MR | Zbl

[5] R.G. Newton - Scattering theory of waves and particles , McGraw Hill , New York , 1966 . | MR | Zbl

[6] M. Reed et B. Simon - Methods of mathematical physics , Academic Press , New York : vol.I : Functional analysis , 1972 ; vol.II : Fourier analysis , self-adjointness , 1975 ; vol.III : Scattering theory , 1979 ; vol.IV : Analysis of operators , 1978 . | MR

[7] I.M. Sigal , Mathematical foundations of quantum scattering theory for multiparticle systems , Memoirs Amer. Math. Soc. , vol. 209 , Providence , 1978 . | MR | Zbl

[8] W. Thirring et P. Urban (éditeurs) - The Schrödinger equation, Springer , Wien , 1977 . | Zbl

[9] W. Amrein et D.B. Pearson - A time-dependent approach to the total scattering cross-section , à paraître. | Zbl

[10] J.M. Cook - Convergence to the Møller wave matrix , Journ. Math. Phys. 36 (1957) , p. 82-87 . | MR

[11] M.N. Haak - On the convergence to the Møller wave operators , Nuovo Cimento , X Ser. 13 (1959) , p. 231-236 .

[12] J. Jauch - Theory of the scattering operator , Helv. Phys. Acta , 31 (1958) , p. 127-158 . | MR | Zbl

[13] T. Kato - Wave operators and unitary equivalence , Pac. Journ. Math. , 15 (1965) , p. 171-180 . | MR | Zbl

[l4] S.T. Kuroda - On the existence and the unitary property of the scattering operator, Nuovo Cimento , X Ser. 12 (1959) , p. 431-454 . | Zbl

[15] S.T. Kuroda - Scattering theory for differential operators I : Operator theory , Journ. Math. Soc. Japan , 25 (1973) , p. 75-104 ; | MR | Zbl

II : Self-adjoint elliptic operators , ibid. p. 222-234 .

[16] C. Møller - Général properties of the characteristic matria in the theory of elementary particles , Danske Vid. Selsk. Mat.-Fys. Medd. 22 (1946) , no. 19 . | Zbl

[17] L.D. Faddeev - On the Friedrichs model in the perturbation theory of continuous spectrum , Trudy Math. Inst. Steklov , 73 (1964) , p. 292-313 [en russe] . | MR | Zbl

[18] K.O. Friedrichs - On the perturbation of continuous spectra , Comm. Pure Appl. Math. 1 (1948) , p. 361-406 . | MR | Zbl

[19] J.S. Howland - Banach space techniques in the perturbation theory of self-adjoint operators with continuous spectra , Journ. Math. Anal. and Appl., 20 ( 1967) , p. 22-47 . | MR | Zbl

[20] T. Kato et S.T. Kuroda - Theory of simple scattering and eigenfunction expansions , in "Functional Analysis and Related Fields" (F.E. Browder éditeur) , Springer , New York , 1970 . | MR | Zbl

[21] T. Kato et S.T. Kuroda - The abstract theory of scattering , Rocky Mount. Journ. Math., 1 (1971) , p. 127-171 . | MR | Zbl

[22] S.T. Kuroda - An abstract stationary approach to perturbation of continuous spectra and scattering theory , Journ. Math. Anal. and Appl., 20 ( 1967) , p. 57-117 . | MR | Zbl

[23] P.A. Rejto - On gentle perturbations , Comm. Pure Appl. Math. , I : 16 (1963) , p. 279-303 ; II : 17 (1964) , p. 257-292 . | Zbl

[24] P.A. Rejto - On partly gentle perturbations , Journ. Math. Anal. and Appl., I : 17 (1967) , p. 453-462 ; II : 20 (1967) , p. 145-187 ; III : 27 (1969) , p. 21-67 . | Zbl

[25] S. Agmon - Spectral properties of Schrödinger operators , Actes Congrès Internat. Math. Nice , 1970 , vol. 2 , p. 679-684 . | MR | Zbl

[26] S. Agmon - Spectral properties of Schrödinger operators and scattering theory , Annali Scuola Norm. Sup. Pisa , Cl. Sci. II , 2 (1976) , p. 151-218 . | Numdam | MR | Zbl

[27] S. Agmon - Some new results in spectral and scattering theory of differential operators on Rn , Séminaire Goulaouic-Schwartz , Ecole Polytechnique , 1978 . | Numdam | Zbl

[28] S. Agmon et L. Hörmander - Asymptotic properties of solutions of differential equations with simple characteristics, Journ. Anal. Math. 30 ( 1976) , p. 1-38 . | MR | Zbl

[29] P. Alsholm et T. Kato - Scattering with long range potentials , in "Partial differential equations" , Proc. Symp. Pure Math. , vol. 23 , Amer. Math. Soc. , Providence , 1973 . | MR | Zbl

[30] W. Amrein et V. Georgescu - On the characterization of bound states and scattering states in quantum mechanics , Helv. Phys. Acta , 46 ( 1973) , p. 635-658 . | MR

[31] A.M. Berthier et P. Collet - Existence and completeness of the wave operators in scattering theory with momentum-dependent potentials , Journ. Funct. Anal. , 26 (1977) , p. 1-15 . | MR | Zbl

[32] A.M. Berthier et P. Collet - Wave operators for momentum dependent long range potentials , Ann. Inst. Henri Poincaré , série A , 26 (1977) , p. 279-293 . | Numdam | MR | Zbl

[33] H. Brezis et T. Kato - Remarks on the Schrödinger operator with singular complex potentials , à paraître . | Zbl

[34] P.J. Deift et B. Simon - A time-dependent approach to the completeness of multiparticle quantum systems , Comm. Pure Appl. Math. , 30 (1977) , p. 573-583 . | MR | Zbl

[35] J. Dollard - Asymptotic convergence and the Coulomb interaction , Journ. Math. Phys. 5 (1964) , p. 729-738 . | MR

[36] J. Dollard - Quantum mechanical scattering theory for short-range and Coulomb interaction, Rocky Mount. Journ. Math., 1 (1971) , p. 5-88 . | MR | Zbl

[37] V. Enss - Asymptotic completeness for quantum mechanical potential scattering , I : Short range potentials , Comm. Math. Phys., 61 (1978) , p. 285-291 ; II : Singular and long range potentials , à paraître aux Ann. Phys. | MR | Zbl

[38] L. Hormander - The existence of wave operators in scattering theory , Math. Zeit., 146 (1976) , p. 69-91 . | MR | Zbl

[39] T. Ikebe - Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory, Arch. Rat. Mech. Anal., 5 (1960) , p. 1-34 . | MR | Zbl

[40] J. Jauch et I. Zinnes - The asymptotic condition for simple scattering systems , Nuovo Cimento . X Ser. 11 (1959) , p. 553-567 . | MR

[41] R.B. Lavine - Absolute continuity of positive spectrum for Schrödinger operators with long range potentials , Journ. Funct. Anal., 12 (1973) , p. 30-54 . | MR | Zbl

[42] D. Ruelle - A remark on bound states in potential scattering theory , Nuovo Cimento, 61A ( 1969) , p. 655-662 . | MR

[43] B. Simon - Geometric methods in multiparticle quantum systems, Comm. Math. Phys., 55 (1977) , p. 259-274 . | MR | Zbl

[44] B. Simon - Phase space analysis of simple scattering systems , extension of some work of Enss , à paraître au Duke Math. Journ. | Zbl

[2 bis] L.D. Faddeev - Mathematical aspects of the three body problem in quantum scattering theory, Israël program for scientific translation, 1965.] | MR | Zbl