Absence of discrete spectrum of the Schrödinger operators of positive molecular ions
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 94-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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For multiatomic positive molecular ions with $N$ electrons and charges $Z_i$ of the nuclei it is shown that there are no bound states for $Z_i>\gamma N$ for some $\gamma$. It is also shown that the discrete spectrum of the Schrödinger operator of a molecular ion is empty if for at least some of the nuclei the condition $Z_i\gg N$ is satisfied, whereas the charges of the other nuclei can be small.
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     title = {Absence of discrete spectrum of the {Schr\"odinger} operators of positive molecular ions},
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S. A. Vugal'ter. Absence of discrete spectrum of the Schrödinger operators of positive molecular ions. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 94-106. http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a7/

[1] Ruskai M. B., Lett. in Math. Phys., 19 (1989), 121–132 | DOI | MR

[2] Ruskai M. B., Commun. Math. Phys., 137 (1991), 553–566 | DOI | MR | Zbl

[3] Vugal'ter S. A., Zhislin G. M., Rep. on Math. Phys., 19 (1984), 39–90 | DOI | MR | Zbl

[4] Vugalter S. A., Zhislin G. M., Trudy Mosk. matem. obschestva, 49 (1986), 95–112 | MR

[5] Vugalter S. A., Zhislin G. M., TMF, 55:1 (1983), 66–77 | MR

[6] Antonets M. A., Zhislin G. M., Shereshevskii I. A., “O diskretnom spektre $N$-chastichnykh gamiltonianov”, Prilozh. k knige: Iorgens I., Vaidman K., Spektralnye svoistva gamiltonovykh operatorov, Mir, M., 1976 | MR

[7] Sigalov A. G., Sigal I. M., TMF, 5:1 (1970), 73–93 | MR

[8] Vugalter S. A., Zhislin G. M., Trudy Mosk. matem. obschestva, 54 (1991), 187–213 | MR

[9] Zhislin G. M., Izv. AN SSSR. Ser. matem., 33:3 (1969), 590–649 | MR | Zbl