Théorie de la diffusion pour l'équation de Schrödinger
Séminaire Bourbaki (1978-1979)
- Volume: 21, page 132-150
- ISSN: 0303-1179
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topCartier, Pierre. "Théorie de la diffusion pour l'équation de Schrödinger." Séminaire Bourbaki 21 (1978-1979): 132-150. <http://eudml.org/doc/109932>.
@article{Cartier1978-1979,
author = {Cartier, Pierre},
journal = {Séminaire Bourbaki},
keywords = {Schrödinger operator; spectrum; diffusion; asymptotic behavior of solutions},
language = {fre},
pages = {132-150},
publisher = {Springer-Verlag},
title = {Théorie de la diffusion pour l'équation de Schrödinger},
url = {http://eudml.org/doc/109932},
volume = {21},
year = {1978-1979},
}
TY - JOUR
AU - Cartier, Pierre
TI - Théorie de la diffusion pour l'équation de Schrödinger
JO - Séminaire Bourbaki
PY - 1978-1979
PB - Springer-Verlag
VL - 21
SP - 132
EP - 150
LA - fre
KW - Schrödinger operator; spectrum; diffusion; asymptotic behavior of solutions
UR - http://eudml.org/doc/109932
ER -
References
top- [1] V. de Alfaro et T. Regge - Potential scattering , North Holland , Amsterdam , 1965. Zbl0141.23202
- [2] W. Amrein , J. Jauch , K. Sinha - Scattering theory in quantum mechanics , Benjamin, New York , 1977 . Zbl0376.47001MR495999
- [3] K.O. Friedrichs - Perturbation of spectra in Hilbert space , Amer. Math. Soc. Lect. in Appl. Math. , vol. 3 , Providence , 1965 . Zbl0142.11001MR182883
- [4] T. Kato - Perturbation theory for linear operators , 2e édit. , Springer , New York, 1976 . Zbl0148.12601MR407617
- [5] R.G. Newton - Scattering theory of waves and particles , McGraw Hill , New York , 1966 . Zbl0496.47011MR221823
- [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 . MR529429
- [7] I.M. Sigal , Mathematical foundations of quantum scattering theory for multiparticle systems , Memoirs Amer. Math. Soc. , vol. 209 , Providence , 1978 . Zbl0399.47008MR508478
- [8] W. Thirring et P. Urban (éditeurs) - The Schrödinger equation, Springer , Wien , 1977 . Zbl0354.00014
- [9] W. Amrein et D.B. Pearson - A time-dependent approach to the total scattering cross-section , à paraître. Zbl0415.47006
- [10] J.M. Cook - Convergence to the Møller wave matrix , Journ. Math. Phys.36 (1957) , p. 82-87 . MR91746
- [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 . Zbl0081.43304MR94163
- [13] T. Kato - Wave operators and unitary equivalence , Pac. Journ. Math. , 15 (1965) , p. 171-180 . Zbl0125.34902MR180138
- [l4] S.T. Kuroda - On the existence and the unitary property of the scattering operator, Nuovo Cimento , X Ser. 12 (1959) , p. 431-454 . Zbl0084.44801
- [15] S.T. Kuroda - Scattering theory for differential operators I : Operator theory , Journ. Math. Soc. Japan , 25 (1973) , p. 75-104 ; Zbl0245.47006MR326435
- II : Self-adjoint elliptic operators , ibid. p. 222-234 . Zbl0252.47007
- [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 . Zbl0063.04067
- [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] . Zbl0148.12801MR178362
- [18] K.O. Friedrichs - On the perturbation of continuous spectra , Comm. Pure Appl. Math.1 (1948) , p. 361-406 . Zbl0031.31204MR29100
- [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 . Zbl0152.33901MR218927
- [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 . Zbl0224.47004MR385603
- [21] T. Kato et S.T. Kuroda - The abstract theory of scattering , Rocky Mount. Journ. Math., 1 (1971) , p. 127-171 . Zbl0241.47005MR385604
- [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 . Zbl0153.16903MR216331
- [23] P.A. Rejto - On gentle perturbations , Comm. Pure Appl. Math. , I : 16 (1963) , p. 279-303 ; II : 17 (1964) , p. 257-292 . Zbl0133.08002
- [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 . Zbl0158.14801
- [25] S. Agmon - Spectral properties of Schrödinger operators , Actes Congrès Internat. Math.Nice , 1970 , vol. 2 , p. 679-684 . Zbl0228.47031MR510045
- [26] S. Agmon - Spectral properties of Schrödinger operators and scattering theory , Annali Scuola Norm. Sup. Pisa , Cl. Sci. II , 2 (1976) , p. 151-218 . Zbl0315.47007MR397194
- [27] S. Agmon - Some new results in spectral and scattering theory of differential operators on Rn , Séminaire Goulaouic-Schwartz , Ecole Polytechnique , 1978 . Zbl0406.35052
- [28] S. Agmon et L. Hörmander - Asymptotic properties of solutions of differential equations with simple characteristics, Journ. Anal. Math.30 ( 1976) , p. 1-38 . Zbl0335.35013MR466902
- [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 . Zbl0263.47008MR385351
- [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 . MR363267
- [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 . Zbl0358.35064MR454404
- [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 . Zbl0346.47010MR462329
- [33] H. Brezis et T. Kato - Remarks on the Schrödinger operator with singular complex potentials , à paraître . Zbl0408.35025
- [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 . Zbl0354.47004MR459397
- [35] J. Dollard - Asymptotic convergence and the Coulomb interaction , Journ. Math. Phys.5 (1964) , p. 729-738 . MR163620
- [36] J. Dollard - Quantum mechanical scattering theory for short-range and Coulomb interaction, Rocky Mount. Journ. Math., 1 (1971) , p. 5-88 . Zbl0226.35074MR270673
- [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. Zbl0389.47005MR523013
- [38] L. Hormander - The existence of wave operators in scattering theory , Math. Zeit., 146 (1976) , p. 69-91 . Zbl0319.35059MR393884
- [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 . Zbl0145.36902MR128355
- [40] J. Jauch et I. Zinnes - The asymptotic condition for simple scattering systems , Nuovo Cimento . X Ser. 11 (1959) , p. 553-567 . MR107498
- [41] R.B. Lavine - Absolute continuity of positive spectrum for Schrödinger operators with long range potentials , Journ. Funct. Anal., 12 (1973) , p. 30-54 . Zbl0246.47017MR342880
- [42] D. Ruelle - A remark on bound states in potential scattering theory , Nuovo Cimento, 61A ( 1969) , p. 655-662 . MR246603
- [43] B. Simon - Geometric methods in multiparticle quantum systems, Comm. Math. Phys., 55 (1977) , p. 259-274 . Zbl0413.47008MR496073
- [44] B. Simon - Phase space analysis of simple scattering systems , extension of some work of Enss , à paraître au Duke Math. Journ. Zbl0402.35076
- [2 bis] L.D. Faddeev - Mathematical aspects of the three body problem in quantum scattering theory, Israël program for scientific translation, 1965.] Zbl0131.43504MR221828
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