Skip to main content
SpringerLink
Log in

Théorie de la diffusion pour l'equation de Schrödinger

  • Conference paper
  • First Online:
Séminaire Bourbaki vol. 1978/79 Exposés 525 – 542

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 770))

  • 180 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

A. Ouvrages généraux

  1. V. de ALFARO et T. REGGE-Potential scattering, North Holland, Amsterdam, 1965.

    MATH  Google Scholar 

  2. W. AMREIN, J. JAUCH, K. SINHA-Scattering theory in quantum mechanics, Benjamin, New York, 1977.

    MATH  Google Scholar 

  3. K.O. FRIEDRICHS-Perturbation of spectra in Hilbert space, Amer. Math. Soc. Lect. in Appl. Math., vol. 3, Providence, 1965.

    Google Scholar 

  4. T. KATO-Perturbation theory for linear operators, 2e édit., Springer, New York, 1976.

    MATH  Google Scholar 

  5. R.G. NEWTON-Scattering theory of waves and particles, McGraw Hill, New York, 1966.

    MATH  Google Scholar 

  6. vol.I: Functional analysis, 1972

    MATH  Google Scholar 

  7. vol.II: Fourier analysis, self-adjointness, 1975

    MATH  Google Scholar 

  8. vol.III: Scattering theory, 1979

    MATH  Google Scholar 

  9. vol.IV: Analysis of operators, 1978.

    MATH  Google Scholar 

  10. I.M. SIGAL, Mathematical foundations of quantum scattering theory for multiparticle systems, Memoirs Amer. Math. Soc., vol. 209, Providence, 1978.

    Google Scholar 

  11. W. THIRRING et P. URBAN (éditeurs)-The Schrödinger equation, Springer, Wien, 1977.

    MATH  Google Scholar 

B. Méthodes non-stationnaires

  1. W. AMREIN et D.B. PEARSON-A time-dependent approach to the total scattering cross-section, à paraître.

    Google Scholar 

  2. J.M. COOK-Convergence to the Møller wave matrix, Journ. Math. Phys. 36 (1957), p. 82–87.

    Google Scholar 

  3. M.N. HAAK-On the convergence to the Møller wave operators, Nuovo Cimento, X Ser. 13 (1959), p. 231–236.

    Google Scholar 

  4. J. JAUCH-Theory of the scattering operator, Helv. Phys. Acta, 31 (1958), p. 127–158.

    MATH  MathSciNet  Google Scholar 

  5. T. KATO-Wave operators and unitary equivalence, Pac. Journ. Math., 15 (1965), p. 171–180.

    MATH  Google Scholar 

  6. S.T. KURODA-On the existence and the unitary property of the scattering operator, Nuovo Cimento, X Ser. 12 (1959), p. 431–454.

    MATH  Google Scholar 

  7. S.T. KURODA-Scattering theory for differential operators I: Operator theory, Journ. Math. Soc. Japan, 25 (1973), p. 75–104; II: Self-adjoint elliptic operators, ibid. p. 222–234.

    MATH  MathSciNet  Google Scholar 

  8. C. MØLLER-General properties of the characteristic matrix in the theory of elementary particles, Danske Vid. Selsk. Mat.-Fys. Medd. 22 (1946), no. 19.

    Google Scholar 

C. Méthodes stationnaires

  1. 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].

    MATH  MathSciNet  Google Scholar 

  2. K.O. FRIEDRICHS-On the perturbation of continuous spectra, Comm. Pure Appl. Math. 1 (1948), p. 361–406.

    MATH  MathSciNet  Google Scholar 

  3. 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.

    Article  MATH  MathSciNet  Google Scholar 

  4. 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.

    Google Scholar 

  5. T. KATO et S.T. KURODA-The abstract theory of scattering, Rocky Mount. Journ. Math., 1 (1971), p. 127–171.

    MATH  MathSciNet  Google Scholar 

  6. 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.

    MATH  MathSciNet  Google Scholar 

  7. P.A. REJTO-On gentle perturbations, Comm. Pure Appl. Math., I: 16 (1963), p. 279–303; II: 17 (1964), p. 257–292.

    MathSciNet  Google Scholar 

  8. 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.

    MathSciNet  Google Scholar 

D. Equation de Schrödinger

  1. S. AGMON-Spectral properties of Schrödinger operators, Actes Congrès Internat. Math. Nice, 1970, vol. 2, p. 679–684.

    Google Scholar 

  2. S. AGMON-Spectral properties of Schrödinger operators and scattering theory, Annali Scuola Norm. Sup. Pisa, Cl. Sci. II, 2 (1976), p. 151–218.

    MathSciNet  Google Scholar 

  3. S. AGMON-Some new results in spectral and scattering theory of differential operators on Rn, Séminaire Goulaouic-Schwartz, Ecole Polytechnique, 1978.

    Google Scholar 

  4. S. AGMON et L. HÖRMANDER-Asymptotic properties of solutions of differential equations with simple characteristics, Journ. Anal. Math. 30 (1976), p. 1–38.

    Article  MATH  Google Scholar 

  5. 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.

    Google Scholar 

  6. 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.

    MathSciNet  Google Scholar 

  7. 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.

    Article  MATH  MathSciNet  Google Scholar 

  8. 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.

    MATH  MathSciNet  Google Scholar 

  9. H. BREZIS et T. KATO-Remarks on the Schrödinger operator with singular complex potentials, à paraître.

    Google Scholar 

  10. 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.

    MATH  MathSciNet  Google Scholar 

  11. J. DOLLARD-Asymptotic convergence and the Coulomb interaction, Journ. Math. Phys. 5 (1964), p. 729–738.

    Article  MathSciNet  Google Scholar 

  12. J. DOLLARD-Quantum mechanical scattering theory for short-range and Coulomb interaction, Rocky Mount. Journ. Math., 1 (1971), p. 5–88.

    Article  MATH  MathSciNet  Google Scholar 

  13. 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.

    Article  MATH  MathSciNet  Google Scholar 

  14. L. HÖRMANDER-The existence of wave operators in scattering theory, Math. Zeit., 146 (1976), p. 69–91.

    Article  MATH  Google Scholar 

  15. T. IKEBE-Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory, Arch. Rat. Mech. Anal., 5 (1960), p. 1–34.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. JAUCH et I. ZINNES-The asymptotic condition for simple scattering systems, Nuovo Cimento, X Ser. 11 (1959), p. 553–567.

    MathSciNet  Google Scholar 

  17. R.B. LAVINE-Absolute continuity of positive spectrum for Schrödinger operators with long range potentials, Journ. Funct. Anal., 12 (1973), p. 30–54.

    Article  MATH  MathSciNet  Google Scholar 

  18. D. RUELLE-A remark on bound states in potential scattering theory, Nuovo Cimento, 61A (1969), p. 655–662.

    MathSciNet  Google Scholar 

  19. B. SIMON-Geometric methods in multiparticle quantum systems, Comm. Math. Phys., 55 (1977), p. 259–274.

    Article  MATH  MathSciNet  Google Scholar 

  20. B. SIMON-Phase space analysis of simple scattering systems, extension of some work of Enss, à paraître au Duke Math. Journ.

    Google Scholar 

Référence supplémentaire

  1. L.D. FADDEEV-Mathematical aspects of the three body problem in quantum scattering theory, Israël program for scientific translation, 1965.

    Google Scholar 

Download references

Authors
  1. Pierre Cartier
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1980 N. Bourbaki

About this paper

Cite this paper

Cartier, P. (1980). Théorie de la diffusion pour l'equation de Schrödinger. In: Séminaire Bourbaki vol. 1978/79 Exposés 525 – 542. Lecture Notes in Mathematics, vol 770. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0096240

Download citation

  • DOI: https://doi.org/10.1007/BFb0096240

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09733-4

  • Online ISBN: 978-3-540-38547-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation