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.
@article{FAA_2015_49_2_a9,
author = {G. M. Zhislin},
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},
pages = {85--88},
year = {2015},
volume = {49},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a9/}
}
TY - JOUR AU - G. M. Zhislin TI - On the discrete spectrum of the Hamiltonians of $n$-particle systems with $n\to\infty$ in function spaces with various permutation symmetries JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 2015 SP - 85 EP - 88 VL - 49 IS - 2 UR - http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a9/ LA - ru ID - FAA_2015_49_2_a9 ER -
%0 Journal Article %A G. M. Zhislin %T On the discrete spectrum of the Hamiltonians of $n$-particle systems with $n\to\infty$ in function spaces with various permutation symmetries %J Funkcionalʹnyj analiz i ego priloženiâ %D 2015 %P 85-88 %V 49 %N 2 %U http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a9/ %G ru %F FAA_2015_49_2_a9
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/