Abstract
We consider a two-dimensional periodic Schrödinger operator perturbed by the interaction potential of two one-dimensional particles. We prove that quasilevels (i.e., eigenvalues or resonances) of the given operator exist for a fixed quasimomentum and a small perturbation near the band boundaries of the corresponding periodic operator. We study the asymptotic behavior of the quasilevels as the coupling constant goes to zero. We obtain a simple condition for a quasilevel to be an eigenvalue.
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References
S. M. Mahajan and A. Thyagaraja, J. Phys. A, 39, 667–671 (2006).
G. V. Wolf and Yu. P. Chuburin, Phys. Solid State, 47, 1048–1052 (2005).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Acad. Press, New York (1978).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis, Acad. Press, New York (1972).
Yu. P. Chuburin, Theor. Math. Phys., 110, 351–359 (1997).
R. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, New York (1965).
Yu. P. Chuburin, Theor. Math. Phys., 98, 27–33 (1994).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 115–125, January, 2009.
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Chuburin, Y.P. Quasilevels of a two-particle Schrödinger operator with a perturbed periodic potential. Theor Math Phys 158, 96–104 (2009). https://doi.org/10.1007/s11232-009-0007-5
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DOI: https://doi.org/10.1007/s11232-009-0007-5