On continuous spectrum eigenfunctions asymptotic behaviour at infinity in configuration space for the system of three three-dimensional like-charged quantum particles
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 79-115
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To our knowledge there are no complete results, even not strictly mathematically justified, related to the system of three and more quantum particles, interacting by Coulomb pair potentials, and expressed in terms of eigenfunctions. For the system of three such identical particles we suggest the asymptotic formulas describing the behaviour of eigenfunctions at infinity in configuration space.
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S. B. Levin. On continuous spectrum eigenfunctions asymptotic behaviour at infinity in configuration space for the system of three three-dimensional like-charged quantum particles. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 79-115. http://geodesic.mathdoc.fr/item/ZNSL_2016_451_a6/

[1] V. S. Buslaev, S. P. Merkurev, S. P. Salikov, Problemy matem. fiziki, 9, Leningr. Universitet, Leningrad, 1979, 14–30

[2] D. R. Yafaev, Matematicheskaya teoriya rasseyaniya, Izdatelstvo S.-Peterburgskogo Universiteta, S.-Peterburg, 1994 | MR

[3] L. D. Faddeev, “Matematicheskie aspekty zadachi trekh tel v kvantovoi teorii rasseyaniya”, ZhETF, 39:5 (1960), 1459–1467

[4] V. S. Buslaev, S. P. Merkurev, S. P. Salikov, “Granichnye zadachi matematicheskoi fiziki i smezhnye voprosy v teorii funktsii. 11”, Zap. Nauchn. Sem. LOMI, 84, 1979, 16–22 | MR | Zbl

[5] V. S. Buslaev, N. A. Kaliteevskii, TMF, 70:2 (1987), 266–277 | MR

[6] M. Brauner, J. S. Briggs, H. Klar, J. Phys. B, 22 (1989), 2265–2287 | DOI

[7] V. S. Buslaev, S. B. Levin, Selected topics in mathematical physics, Amer. Math. Soc. Transl. (2), 225, 2008, 55–71 | DOI | Zbl

[8] V. S. Buslaev, S. B. Levin, P. Neittaannmäki, T. Ojala, J. Phys. A: Math. Theor., 43 (2010), 285205 | DOI | MR | Zbl

[9] V. S. Buslaev, S. B. Levin, Algebra i analiz, 22:3 (2010), 60–79 | MR | Zbl

[10] V. S. Buslaev, S. B. Levin, Funktsionalnyi analiz i ego prilozheniya, 46:2 (2012), 83–88 | DOI | MR | Zbl

[11] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Gos. izd-vo fiz-mat. lit-ry, 1963

[12] V. S. Buslaev, Problemy matematicheskoi fiziki, v. 1, Spektralnaya teoriya i volnovye protsessy, Izd-vo Leningradskogo Universiteta, Leningrad, 1966, 82–101

[13] S. P. Merkurev, Yadernaya fizika, 24 (1976), 289

[14] S. P. Merkurev, Teor. Mat. Fiz., 32:2 (1977), 187–207 | MR

[15] S. P. Merkurev, L. D. Faddeev, Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, Glav. red. fiz.-mat. lit., M., 1985

[16] E. O. Alt, A. M. Mukhamedzhanov, JETP Lett., 56:9 (1992), 435–439 | MR

[17] E. O. Alt, A. M. Mukhamedzhanov, Phys. Rev. A, 47 (1993), 2004 | DOI | MR

[18] G. Garibotti, J. E. Miraglia, Phys. Rev. A, 21 (1980), 572 | DOI

[19] A. L. Godunov, Sh. D. Kunikeev, V. N. Mileev, V. S. Senashenko, Proc. 13th Int. Conf. on Physics of electronic and atomic collisions, Abstracts (Berlin), ed. J. Eichler, Noth holland, Amsterdam, 1983, 380

[20] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 1, Nauka, Moskva, 1965

[21] M. Abramowitz, I. Stegun, Handbook of mathematical functions, New York, 1965 | MR

[22] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Moskva, 1959