Geodesic
Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a~given symmetry
Izvestiya. Mathematics , Tome 3 (1969) no. 3, pp. 559-616.

Voir la notice de l'article provenant de la source Math-Net.Ru

The energy operator of a molecule-type system is investigated in the spaces of functions of given permutational, rotational, and reflection symmetry; a necessary and sufficient condition is found for the existence of a discrete spectrum and the limit spectrum is determined. In addition, the existence is proved of an infinite sequence of points of the discrete spectrum of an atom when allowance is made for the motion of the nucleus. 
@article{IM2_1969_3_3_a5,
     author = {G. M. Zhislin},
     title = {Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a~given symmetry},
     journal = {Izvestiya. Mathematics },
     pages = {559--616},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a5/}
}
TY  - JOUR
AU  - G. M. Zhislin
TI  - Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a~given symmetry
JO  - Izvestiya. Mathematics 
PY  - 1969
SP  - 559
EP  - 616
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a5/
LA  - en
ID  - IM2_1969_3_3_a5
ER  - 
%0 Journal Article
%A G. M. Zhislin
%T Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a~given symmetry
%J Izvestiya. Mathematics 
%D 1969
%P 559-616
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a5/
%G en
%F IM2_1969_3_3_a5
G. M. Zhislin. Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a~given symmetry. Izvestiya. Mathematics , Tome 3 (1969) no. 3, pp. 559-616. http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a5/

[1] Zhislin G. M., Sigalov A. G., “O spektre operatora energii dlya atomov s nepodvizhnymi yadrami na podprostranstvakh, otvechayuschikh neprivodimym predstavleniyam gruppy perestanovok”, Izv. AN SSSR. Ser. matem., 29 (1965), 835–860 | MR | Zbl

[2] Zhislin G. M., Sigalov A. G., “O nekotorykh matematicheskikh zadachakh teorii atomnykh spektrov”, Izv. AN SSSR. Ser. matem., 29 (1965), 1261–1272 | MR | Zbl

[3] Iörgens K., Über das wesentliche Spectrum elliptischen Differentialgleichungen von Schrödinger-Typ, Universität Heidelberg, Institut für Angew. Math., 1965

[4] Zhislin G. M., Issledovanie spektra operatora Shredingera, dissertatsiya, 1960

[5] Sigalov A. G., “Ob osnovnoi matematicheskoi zadache teorii atomnykh spektrov”, Uspekhi matem. nauk, XXII:2(134), 1–20

[6] Murnagan F., Teoriya predstavlenii grupp, IL, M., 1950

[7] Neimark M. A., Lineinye predstavleniya gruppy Lorentsa, Fizmatgiz, M., 1958 | MR

[8] Vigner E., Teoriya grupp i ee prilozheniya k kvantovomekhanicheskoi teorii atomnykh spektrov, IL, M., 1961

[9] Ikeebe T., Kato T., “Uniquenes of the selfadjoint extension of singular elliptic differential operators”, Arch. for Rat. Mech. and An., 9:1 (1962), 77–92 | MR

[10] Stummel F., “Singuläre elliptische Differentialoperatoren in Hilberstschen Räumen”, Math. Ann., 132 (1956), 150–176 | DOI | MR | Zbl

[11] Gelfand I. M., Minlos R. A., Shapiro Z. Ya., Predstavleniya gruppy vraschenii i gruppy Lorentsa, Fizmatgiz, M., 1958

[12] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, LGU, L., 1950

[13] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, IL, M., 1954

[14] Zhislin G. M., “Issledovanie spektra operatora Shredingera dlya sistemy mnogikh chastits”, Tr. Mosk. matem. ob-va, 9 (1960), 81–120 | Zbl

[15] Gombash P., Problema mnogikh chastits v kvantovoi mekhanike, IL, M., 1952

[16] Zhislin G. M., “Ob uzlakh sobstvennykh funktsii operatora Shredingera”, Uspekhi matem. nauk, 16:1(97), 149–152 | Zbl

[17] Khamermesh M., Teoriya grupp i ee primenenie k fizicheskim problemam, Mir, M., 1966 | Zbl

[18] Berezanskii Yu. M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR

[19] Zhislin G. M., “Kharakteristika spektra operatorov Shredingera dlya sistem tipa molekul”, Dokl. AN SSSR, 128:2 (1959), 231–234 | Zbl

[20] Zhislin G. M., “O spektre operatora energii sistem tipa molekul na prostranstvakh funktsii zadannoi simmetrii”, Dokl. AN SSSR, 175:3 (1967), 521–524 | Zbl

[21] Kato T., “Fundamental properties of Hamiltonion operators of Schrödinger type”, Trans. Amer. Math. Soc., 70:2 (1951), 195–211 | DOI | MR | Zbl

[22] Hunziker W., “On the Spectra of Schrödinger Multiparticle Hamiltonians”, Helv. phys. acta, 39:5 (1966), 451–462 | MR | Zbl

[23] Kato T., “Some Mathematical Problems in Quantum Mechanics”, Supplement of the Progress of Theoret. Physics, 40 (1967), 3–18 | DOI | MR

[24] Weidmann J., “The Virial theorem and its application to the spectral theory of Schrödinger operators”, Bull. Amer. Math. Soc., 73:3 (1967), 452–456 | DOI | MR | Zbl