Virtual levels of $n$-particle systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 2, pp. 265-275
Voir la notice de l'article provenant de la source Math-Net.Ru
The energy operators $H$ of unstable quantum systems $Z_1$ that do not possess stable subsystems are considered. It is shown that if the Hamiltonians of
the subsystems in $Z_1$ do not have virtual levels but the operator $H$ does
then a virtual level of the operator $H$ is due to the existence of a finitedimensional subspace of functions $\mathscr W=\{u\}\in\mathscr L_2^{(1)}$ such that the functions $u$ are generalized solutions of the Schrödinger equation $Hu=0$ and on the subspace orthogonal (in the gradient sense) to $\mathscr W$ the operator $H$ does not have virtual levels.
@article{TMF_1986_68_2_a9,
author = {G. M. Zhislin},
title = {Virtual levels of $n$-particle systems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {265--275},
publisher = {mathdoc},
volume = {68},
number = {2},
year = {1986},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1986_68_2_a9/}
}
G. M. Zhislin. Virtual levels of $n$-particle systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 2, pp. 265-275. http://geodesic.mathdoc.fr/item/TMF_1986_68_2_a9/