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Scattering from impurities in a crystal

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Abstract

A time independent scattering theory for a particle in a crystal with impurity is given. It is shown that the scattered wave is the solution of a Lippman Schwinger equation, and that the existence of bound states or narrow resonances is related more to the band structure than to the form of the impurity potential.

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References

  1. Kato, T., Kuroda, S.-T.: Theory of simple scattering and eigenfunction expansions. In: Functional analysis and related fields, Browder (Ed.). Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  2. Kuroda, S.-T.: A stationary method of scattering and some applications. In: Proceedings of the Int. Conf. on Functional Analysis. University of Tokyo Press 1970

  3. Kosicki-Paul, W.: Phys. Rev. Letters17, 246–249 (1966);17, 1175–1177 (1966)

    Google Scholar 

  4. Onton, A.: Phys. Rev.186, 786–790 (1969); B4, 4449–4452 (1971)

    Google Scholar 

  5. Bassani, F.: Theory of imperfect crystalline solids, Trieste lectures, p. 265. Vienna: IAEA 1970

    Google Scholar 

  6. Preziosi, B.: Nuovo Cimento6 B, 131–138 (1971)

    Google Scholar 

  7. Bassani, F., Iadonisi, G., Preziosi, B.: Rept. Progr. Phys.37, Part 3 (1974)

  8. Ikebe, T.: Arch. Rat. Mech. Anal.5, 1–34 (1960)

    Google Scholar 

  9. Simon, B.: Quantum mechanics for Hamiltonians defined as quadratic forms. Princeton: Princeton University Press 1971

    Google Scholar 

  10. Thomas, L.: Commun. math. Phys.33, 339 (1973)

    Google Scholar 

  11. Lenahan, T.A.: On quantum mechanical scattering in periodic media. Ph.D. Thesis, in Applied Mathematics. University of Pennsylvania (1970)

  12. Troianiello, G.: J. Math. Phys.15, 2048 (1974)

    Google Scholar 

  13. Guillot, J.-C.: Report of the Department of Mathematics. University of Paris-Nord (1974)

  14. Avron, J., Grossmann, A., Rodriguez, R.: Rept. Math. Phys.5, 113 (1974)

    Google Scholar 

  15. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  16. Balslev, E.: Math. Scand.19, 193 (1966)

    Google Scholar 

  17. Avron, J., Grossmann, A., Rodriguez, R., Zak, J.: Preprint CNRS-C.P.T. 1975

  18. Callaway, J.: J. Math. Phys.5, 783–798 (1964)

    Google Scholar 

  19. Phillips, J.C.: Phys. Rev.104, 1263 (1956)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Université d'Aix-Marseille II, U.E.R. de Luminy et Centre de Physique Théorique, CNRS Marseille, Marseille, France

    F. Bentosela

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  1. F. Bentosela
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Communicated by W. Hunziker

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Bentosela, F. Scattering from impurities in a crystal. Commun.Math. Phys. 46, 153–166 (1976). https://doi.org/10.1007/BF01608494

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  • DOI: https://doi.org/10.1007/BF01608494

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