Geodesic
Virtual levels of $n$-particle systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 2, pp. 265-275 
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/
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     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},
     year = {1986},
     volume = {68},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_68_2_a9/}
}
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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.

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