Geodesic
Structure of Regular Solutions of the Three-Body Schrödinger Equation near the Pair Impact Point
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 1, pp. 90-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the six-dimensional Schrödinger equation for a three-body system with central pair interactions of a more general form than Coulomb interactions. Regular general and special physical solutions of this equation are represented by infinite asymptotic series in integer powers of the distance between two particles and in the sought functions of the other three-body coordinates. Constructing such functions in angular bases composed of spherical and bispherical harmonics or symmetrized Wigner $D$-functions is reduced to solving simple recursive algebraic equations. For projections of physical solutions on the angular bases functions, we derive boundary conditions at the pair impact point.
Keywords: three-body problem, Schrödinger equation, regular solutions, asymptotic expansions. 
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     author = {V. V. Pupyshev},
     title = {Structure of {Regular} {Solutions} of the {Three-Body} {Schr\"odinger} {Equation} near the {Pair} {Impact} {Point}},
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V. V. Pupyshev. Structure of Regular Solutions of the Three-Body Schrödinger Equation near the Pair Impact Point. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 1, pp. 90-114. http://geodesic.mathdoc.fr/item/TMF_2003_136_1_a6/

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

[2] V. V. Kostrykin, A. A. Kvitsinsky, S. P. Merkuriev, Few-Body Syst., 6 (1989), 97 | DOI | MR

[3] D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Kvantovaya teoriya uglovogo momenta, Nauka, M., 1975

[4] A. F. Nikiforov, V. B. Uvarov, Osnovy teorii spetsialnykh funktsii, Nauka, M., 1974 | MR

[5] S. I. Vinitskii, L. I. Ponomarev, EChAYa, 13 (1982), 1336

[6] V. I. Korobov, YaF, 50 (1989), 1595 | MR

[7] V. I. Korobov, I. V. Puzynin, S. I. Vinitsky, Muon Catalyzed Fusion, 7 (1992), 63

[8] G. I. Marchuk, Metody vychislitelnoi matematiki, Nauka, M., 1989 | MR

[9] P. M. Prenter, Splines and Variational Methods, Wiley, N. Y., 1975 | MR | Zbl

[10] K. Vildermut, Ya. Tan, Edinaya teoriya yadra, Mir, M., 1980 | MR

[11] Yu. S. Zavyalov, B. I. Kvasov, V. L. Miroshnichenko, Metody splain-funktsii, Nauka, M., 1980 | MR

[12] T. Kato, Commun. Pure and Appl. Math., 10 (1957), 151 | DOI | MR | Zbl

[13] W. A. Bingel, Z. Naturforsh. A, 18 (1963), 1249 | MR | Zbl

[14] R. T. Pack, W. B. Brown, J. Chem. Phys., 45 (1966), 556 | DOI

[15] F. T. Smith, J. Chem. Phys., 31 (1959), 1352 | DOI

[16] V. I. Smirnov, Kurs vysshei matematiki, T. 3. Ch. 1, 2, Nauka, M., 1974 | MR

[17] E. S. Chang, U. Fano, Phys. Rev. A, 6 (1972), 173 | DOI