Abstract
One proves the absence of bound states of a two-particle system in the external constant electric field. The conditions on the potential coincide basically with the conditions that ensure the existence of the wave operators.
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Literature cited
A. F. Vakulenko, “The Treves inequality and the absence of positive eigenvalues for the Schrödinger operator with a complex potential,” J. Sov. Math.,37, No. 1 (1987).
J. E. Avron and I. W. Herbst, “Spectral and scattering theory of Schrödinger operators related to the Stark effect,” Commun. Math. Phys.,52, No. 3, 239–254 (1977).
B. Simon, “Phase space analysis of simple scattering systems: extension of some work of Enns,” Duke Math. J.,46, No. 1, 119–168 (1979).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 18–20, 1986.
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Vakulenko, A.F. Absence of bound states for a two-particle system in the external constant electric field. J Math Sci 40, 599–601 (1988). https://doi.org/10.1007/BF01094183
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DOI: https://doi.org/10.1007/BF01094183