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.
Similar content being viewed by others
References
E. B. Davies,Proc. Cambridge Philos. Soc.,82, 327 (1977).
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).
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. IV.Analysis of operators, Academic Press, New York-London (1978).
Yu. P. Chuburin,Teor. Mat. Fiz.,72 (1987).
G. V. Volf, Yu. P. Chuburin, and L. A. Rubtsova,Poverkhnost', No. 10, 81 (1991).
Yu. P. Chuburin,Teor. Mat. Fiz.,102 (1995).
J. Avron and B. Simon,Commun. Math. Phys.,82, 101 (1981).
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. I.Functional Analysis, Academic Press, New York-London (1972).
S. M. Kozlov,Tr. Mosk. Mat. Obshch.,46, 99 (1983).
B. Simon,Bull. Amer. Math. Soc.,7, 447 (1982).
Yu. P. Chuburin,Mat. Zametki,52, 138 (1992).
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. III.Scattering Theory, Academic Press, New York-London (1979).
Yu. P. Chuburin,Teor. Mat. Fiz.,98 (1994).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 1, pp. 133–144, January, 1996.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02070768