Geodesic
Estimates for the interaction potential between two atoms
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 381-396
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We consider a quantum system consisting of two electrons in the Coulomb field of two immovable nuclei spaced at a fixed distance, which is considered the problem parameter. We use spectral theory methods to obtain estimates of the system ground-state energy as a function of the internuclear distance. We obtain part of the results under the assumption that the Coulomb interaction constant between different atoms is small. We discuss the importance of the presented investigation for quantum chemistry.
Keywords: spectrum of the Schrödinger operator, quantum chemistry, hydrogen molecule. 
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V. A. Malyshev; R. A. Minlos. Estimates for the interaction potential between two atoms. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 381-396. http://geodesic.mathdoc.fr/item/TMF_2010_162_3_a3/

[1] R. Bader, Atoms in Molecules. A Quantum Theory, Oxford Univ. Press, Oxford, 1994

[2] R. Grinter, The Quantum in Chemistry: an Experimentalist's View, John Wiley and Sons, West Sussex, UK, 2005

[3] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Fizmatlit, M., 2004 | MR | MR | Zbl

[4] L. Shiff, Kvantovaya mekhanika, IL, M., 1959 | Zbl

[5] O. Sinanoglu, Mnogoelektronnaya teoriya atomov, molekul i ikh vzaimodeistvii, Mir, M., 1966 | DOI

[6] J. M. Combes, R. Seiler, Int. J. Quantum Chem., 14:2 (1978), 213–229 | DOI

[7] G. A. Hagedorn, Comm. Math. Phys., 116:1 (1988), 23–44 | DOI | MR

[8] G. A. Hagedorn, Comm. Math. Phys., 77:1 (1980), 1–19 | DOI | MR | Zbl

[9] R. Seiler, Helv. Phys. Acta, 46 (1973), 230–234

[10] I. V. Komarov, L. I. Ponomarev, S. Yu. Slavyanov, Sferoidalnye i kulonovskie sferoidalnye funktsii, Nauka, M., 1975 | MR

[11] L. D. Faddeev, O. A. Yakubovskii, Lektsii po kvantovoi mekhanike dlya studentov-matematikov, Izd-vo LGU, L., 1980 | MR | Zbl

[12] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, T. 1–4, Mir, M., 1977, 1978, 1982 | MR | MR | MR | Zbl

[13] G. M. Zhislin, Trudy MMO, 9, 1960, 81–120 | MR | Zbl

[14] I. Segal, Bull. Amer. Math. Soc., 75 (1969), 1390–1395 | DOI | MR | Zbl

[15] R. Høegh-Krohn, B. Simon, J. Funct. Anal., 9:2 (1972), 121–180 | DOI | MR

[16] Dzh. Uermer, Teoriya potentsiala, Mir, M., 1980 | MR | MR | Zbl

[17] W. Greiner, Classical Electrodynamics, Classical Theoret. Phys., Springer, New York, 1998 | DOI | MR | Zbl

[18] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | MR | Zbl

[19] K. Fridrikhs, Vozmuschenie spektra operatorov v gilbertovom prostranstve, Mir, M., 1969 | MR | Zbl