Abstract
The restrictions of the nonrelativistic energy operators H n of the relative motion of a system of n identical particles with short-range interaction potentials to subspaces M of functions with various permutation symmetries are considered. It is proved that, for each of these restrictions, there exists an infinite increasing sequence of numbers N j , j = 1, 2, …, such that the discrete spectrum of each operator \(H_{N_j }\) on M is nonempty. The family {M} of considered subspaces is, apparently, close to maximal among those which can be handled by the existing methods of study.
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G. M. Zhislin, Teor. Mat. Fiz., 157:1 (2008), 116–129; English transl.: Theor. Math. Phys., 157:1 (2008), 1461–1473.
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, vol. 3. Quantum Mechanics: Nonrelativistic Theory, Pergamon Press, Oxford, 2013.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 2, pp. 85–88, 2015
Original Russian Text Copyright © by G. M. Zhislin
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Zhislin, G.M. On the discrete spectrum of the Hamiltonians of n-particle systems with n → ∞ in function spaces with various permutation symmetries. Funct Anal Its Appl 49, 148–150 (2015). https://doi.org/10.1007/s10688-015-0098-8
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DOI: https://doi.org/10.1007/s10688-015-0098-8