Geodesic
Spectrum of molecular electron energy operators in spaces of functions of specified symmetry
Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 2, pp. 295-302 
G. M. Zhislin; E. L. Mandel'. Spectrum of molecular electron energy operators in spaces of functions of specified symmetry. Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 2, pp. 295-302. http://geodesic.mathdoc.fr/item/TMF_1969_1_2_a12/
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     title = {Spectrum of molecular electron energy operators in spaces of functions of specified symmetry},
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}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The spectrum of the molecular electron energy operator $H$ is investigated for the case of molecules with fixed nuclei situated such that transformations of the point group $G$ carry identical nuclei into each other. On the spaces of electron wavefuuctions corresponding to the product of irreducible representations of the permutation groups $S_n$ and $G$, the limiting spectrum $H$ is found, and the existence of an infinite number of points of the discrete spectrum is proved for neutral molecules and for positive molecular ions.

[1] G. M. Zhislin, A. G. Sigalov, Izv. AN SSSR, ser. matem., 29:4 (1965), 835 | Zbl

[2] G. M. Zhislin, A. G. Sigalov, Izv. AN SSSR, ser. matem., 29:6 (1965), 1261 | Zbl

[3] G. M. Zhislin, Issledovanie spektra operatora Shredingera dlya sistem mnogikh chastits, Trudy moskovskogo matematicheskogo obschestva, 9, 1960 | MR | Zbl

[4] M. I. Petrashen, E. D. Trifonov, Primenenie teorii grupp v kvantovoi mekhanike, «Nauka», 1967

[5] M. Khammermesh, Teoriya grupp i ee primenenie k fizicheskim problemam, «Mir», 1966

[6] G. M. Zhislin, Izv. AN SSSR, ser. matem., 33 (1969), 590 | Zbl