Geodesic
Three-Particle Problem with Pairwise Interactions Inversely Proportional to Squared Distance
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 268-287 
V. V. Pupyshev. Three-Particle Problem with Pairwise Interactions Inversely Proportional to Squared Distance. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 268-287. http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a8/
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     author = {V. V. Pupyshev},
     title = {Three-Particle {Problem} with {Pairwise} {Interactions} {Inversely} {Proportional} to {Squared} {Distance}},
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     volume = {128},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The hyperharmonic method is used to investigate the three-particle Schrödinger and Faddeev equations with pairwise interactions inversely proportional to the squared distance. Exact solutions for such equations are constructed in the form of a product of the Bessel function depending on the hyperradius and a finite linear combination of the hyperharmonics. A criterion for the existence of such solutions is proved and analyzed.

[1] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Nauka, M., 1974 | MR

[2] S. P. Merkurev, L. D. Faddeev, Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, M., 1985 | MR

[3] V. V. Pupyshev, EChAYa, 30 (1999), 1562

[4] Y. Avishai, J. Math. Phys, 16 (1975), 1491 | DOI

[5] V. V. Pupyshev, Phys. Lett. A, 140 (1989), 151 | DOI | MR

[6] R. I. Dzhibuti, N. B. Krupennikova, Metod gipersfericheskikh funktsii v kvantovoi mekhanike neskolkikh tel, Metsniereba, Tbilisi, 1984 | MR | Zbl

[7] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavleniya grupp, Nauka, M., 1965 | MR

[8] V. V. Pupyshev, YaF, 62 (1999), 1955

[9] J. Raynal, J. Revai, Nuovo Cimento. A, 68 (1970), 612 | DOI | MR

[10] E. Kamke, Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1976 | MR

[11] M. Abramovits, I. Stigan, Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979

[12] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983, S. 581 | MR | Zbl

[13] P. Lankaster, Teoriya matrits, Nauka, M., 1978 | MR

[14] V. V. Voevodin, Vychislitelnye osnovy lineinoi algebry, Nauka, M., 1977 | MR | Zbl

[15] V. V. Pupyshev, Fizicheskie i lozhnye slagaemye tsentralnykh parnykh vzaimodeistvii, Preprint R4-2000-136, OIYaI, Dubna, 2000