On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions
Teoretičeskaâ i matematičeskaâ fizika, Tome 7 (1971) no. 3, pp. 332-341
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Let $H$ be the energy operator of an atom with $n$ electrons in which allowance is made for the motion of the nucleus or the energy operator of $n$ electrons in the field of $n_0$ fixed nuclei. It is shown that in the space of functions defined by an arbitrary irreducible representation of the symmetry group of $H$ the number of discrete eigenvalues of $H$ cannot be infinite if the total charge of the system is less than –1 (in atomic units). Previously, a similar result was known only for $n=2$.
@article{TMF_1971_7_3_a4,
author = {G. M. Zhislin},
title = {On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {332--341},
publisher = {mathdoc},
volume = {7},
number = {3},
year = {1971},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1971_7_3_a4/}
}
TY - JOUR AU - G. M. Zhislin TI - On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1971 SP - 332 EP - 341 VL - 7 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1971_7_3_a4/ LA - ru ID - TMF_1971_7_3_a4 ER -
%0 Journal Article %A G. M. Zhislin %T On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions %J Teoretičeskaâ i matematičeskaâ fizika %D 1971 %P 332-341 %V 7 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1971_7_3_a4/ %G ru %F TMF_1971_7_3_a4
G. M. Zhislin. On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions. Teoretičeskaâ i matematičeskaâ fizika, Tome 7 (1971) no. 3, pp. 332-341. http://geodesic.mathdoc.fr/item/TMF_1971_7_3_a4/