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On the schrödinger equation for a flat film with an asymptotically periodic grating

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Abstract

For a potential asymptotically periodic in x 1 , x 2 and decreasing at |x 3 | → ∞, the Schrödinger equation is solved and some properties of the solutions are described.

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References

  1. E. B. Davies,Proc. Cambridge Philos. Soc.,82, 327 (1977).

    Google Scholar 

  2. Yu. P. Chuburin, “On scattering by a crystal film,” Preprint, Physico-technical Inst. of the Ural Branch of the Acad. of Sci. of the USSR, Sverdlovsk (1985).

  3. M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. IV.Analysis of operators, Academic Press, New York-London (1978).

    Google Scholar 

  4. Yu. P. Chuburin,Teor. Mat. Fiz.,72 (1987).

  5. G. V. Volf, Yu. P. Chuburin, and L. A. Rubtsova,Poverkhnost', No. 10, 81 (1991).

  6. Yu. P. Chuburin,Teor. Mat. Fiz.,102 (1995).

  7. J. Avron and B. Simon,Commun. Math. Phys.,82, 101 (1981).

    Google Scholar 

  8. M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. I.Functional Analysis, Academic Press, New York-London (1972).

    Google Scholar 

  9. S. M. Kozlov,Tr. Mosk. Mat. Obshch.,46, 99 (1983).

    Google Scholar 

  10. B. Simon,Bull. Amer. Math. Soc.,7, 447 (1982).

    Google Scholar 

  11. Yu. P. Chuburin,Mat. Zametki,52, 138 (1992).

    Google Scholar 

  12. M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. III.Scattering Theory, Academic Press, New York-London (1979).

    Google Scholar 

  13. Yu. P. Chuburin,Teor. Mat. Fiz.,98 (1994).

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 1, pp. 133–144, January, 1996.

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Chuburin, Y.P. On the schrödinger equation for a flat film with an asymptotically periodic grating. Theor Math Phys 106, 108–117 (1996). https://doi.org/10.1007/BF02070768

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  • DOI: https://doi.org/10.1007/BF02070768

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