Abstract
For a two-particle Schrödinger operator considered in a cell and having a potential periodic in four variables, we establish the existence of levels (i.e., eigenvalues or resonances) in the neighborhood of singular points of the unperturbed Green’s function and derive an asymptotic formula for these levels. We prove an existence and uniqueness theorem for the solution of the corresponding Lippmann-Schwinger equation.
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M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Acad. Press, New York (1978).
J. R. Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions, Wiley, New York (1972).
Yu. P. Chuburin, Comm. Math. Phys., 249, 497 (2004).
W. Hunziker and I. M. Sigal, J. Math. Phys., 41, 3448 (2000).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory, Acad. Press, New York (1979).
A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics [in Russian], Nauka, Moscow (1984); English transl.: Special Functions of Mathematical Physics: A Unified Introduction with Applications, Birkhäuser, Basel (1988).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis, Acad. Press, New York (1972).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 229–239, May, 2006.
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Chuburin, Y.P. The levels of the two-particle Schrödinger operator corresponding to a crystal film. Theor Math Phys 147, 637–645 (2006). https://doi.org/10.1007/s11232-006-0066-9
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DOI: https://doi.org/10.1007/s11232-006-0066-9