Geodesic
On the discrete spectrum of the Hamiltonians of $n$-particle systems with $n\to\infty$ in function spaces with various permutation symmetries
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 2, pp. 85-88.

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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 $N_j$, $j=1,2,\dots$, 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.
Keywords: many-particle Hamiltonian, discrete spectrum, permutation symmetry. 
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     title = {On the discrete spectrum of the {Hamiltonians} of $n$-particle systems with $n\to\infty$ in function spaces with various permutation symmetries},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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G. M. Zhislin. On the discrete spectrum of the Hamiltonians of $n$-particle systems with $n\to\infty$ in function spaces with various permutation symmetries. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 2, pp. 85-88. http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a9/

[1] G. M. Zhislin, TMF, 157:1 (2008), 116–129 | DOI | MR | Zbl

[2] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika. T. 3. Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1989 | MR