On three-particle integrodifferential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 86-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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Properties of the nonlocal operators $h$ of the system of integrodifferential equations for partial components of the three-particle wave function are explored. By means of expanding the two-variables functions sought for over the known eigen-functions of the $h$ operators the equations of the system are reduced to a system of ordinary second order differential equations for one-variable functions. It is shown that the expansion used is equivalent to the application of hyperharmonic approach to the Faddeev configuration space decomposition of the Schrödinger equation.
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V. V. Pupyshev. On three-particle integrodifferential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 86-93. http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a7/

[1] Kvitsinskii A. A. i dr., EChAYa, 17:3 (1986), 267–290

[2] Faddeev L. D., ZhETF, 39:5 (1960), 1459–1467 | MR

[3] Noyes H. P., Three-Body Problem in Nuclear and Particle Physics, North-Holland, Amsterdam, 1970

[4] Merkurev S. P., Faddeev L. D., Kvantovaya teoriya rasseyaniya v sistemakh neskolkikh chastits, Nauka, M., 1985 | MR

[5] Merkuriev S. P., Gignoux C., Laverne A., Ann. Phys., 99:1 (1976), 30–71 | DOI | MR

[6] Friar J. L., Gibson B. F., Payne G. L., Phys. Rev., 24C:5 (1981), 2279–2289 ; 26C (1982), 1385–1398

[7] Pupyshev V. V., YaF, 43:5 (1986), 1318–1326 | MR

[8] Belyaev V. B., Kartavtsev O. I., Kochkin V. I., Approksimatsiya differentsialnogo operatora uravnenii Faddeeva konechnomernym, Soobschenie R4-84-793, OIYaI, Dubna, 1984; Решение дифференциальных уравнений Фаддеева для задачи рассеяния в системе трех тождественных частиц, Сообщение ОИЯИ Р4-85-816, ОИЯИ, Дубна, 1985

[9] Mandelzweig V. B., Ann. Phys., 104:1 (1977), 1–18 | DOI | MR

[10] Pupyshev V. V., YaF, 43:1 (1986), 260–267 | MR

[11] Lovelace C., Phys. Rev., 132:1 (1963), 483–490

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

[13] Bidenkharn L., Lauk Dzh., Uglovoi moment v kvantovoi fizike, Mir, M., 1984 | MR

[14] Beitman G., Erdeii A., Vysshie transtsendentnye funktsii, T. 1, 2, Nauka, M., 1973 | MR

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

[16] Raynal J., Revai J., Nuovo Cim., 68A:4 (1970), 612–622 | DOI | MR

[17] Fabre de la Ripelle M., Few-Body Systems, 1:4 (1986), 181–190 | DOI | MR

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

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

[20] Smirnov Yu. F., Shitikova K. V., EChAYa, 8:4 (1977), 847–910

[21] Dzhibuti R. I., Metod fazovykh funktsii v kvantovoi mekhanike trekh i chetyrekh tel, Preprint YaF-17, IFAN GSSR, Tbilisi, 1983

[22] Dzhibuti R. I., Tsiklauri Sh. M., YaF, 40:5 (1984), 1171–1179; 41:4 (1985), 865–874 | MR

[23] Kalodzhero F., Metod fazovykh funktsii v teorii potentsialnogo rasseyaniyam, Mir, M., 1979; Бабиков В. В., Метод фазовых функций в квантовой механике, Наука, М., 1976 | MR

[24] Petrov N. M., Pushkash A. M., YaF, 43:6 (1986), 1403–1408

[25] Friar J. L., Gibson B. F., Phys. Rev., 22C:1 (1980), 284–286 | MR

[26] Avishai Y., J. Math. Phys., 16:7 (1975), 1491–1492 | DOI