Abstract
Completeness is proved for systems of two or three quantum particles. The proof is based on the following statement on operators in a Hilbert space. If an operator A is bounded with respect to a self-adjoint operator H and Re((H − λ)f, Af) ≥ ∥Bf∥2, then B is smooth with respect to H.
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Literature cited
M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators, Academic Press, New York (1978).
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 29–36, 1987.
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Vakulenko, A.F. On a variant of commutator estimates in spectral theory. J Math Sci 49, 1136–1139 (1990). https://doi.org/10.1007/BF02208709
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DOI: https://doi.org/10.1007/BF02208709