Geodesic
Model of an effective separable potential in the problem of three one-dimensional quantum particles
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 15-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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Bagmutov A. S., Levin S. B., Toropov B. O. Model of an effective separable potential in the problem of three one-dimensional quantum particles. In this paper, we construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials that support bound states. The asymptotic nature of the solution is determined by the rapid decrease of its residual in the Schr?dinger equation. 
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A. S. Bagmutov; S. B. Levin; V. O. Toropov. Model of an effective separable potential in the problem of three one-dimensional quantum particles. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 15-43. http://geodesic.mathdoc.fr/item/ZNSL_2024_533_a1/

[1] M. Gaudin, B. Derrida, Journal de physique, 36 (1975), 1183–1197 | DOI

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

[3] V. S. Buslaev, S. P. Merkurev, S. P. Salikov, “Granichnye zadachi matematicheskoi fiziki i smezhnye voprosy v teorii funktsii”, Zap. nauchn. sem. POMI, 84, 1979, 16–22 | Zbl

[4] V. S. Buslaev, S. B. Levin, “Selected topics in mathematical physics, Dedicated to Prof. Mikhail Shlëmovich Birman on his 80th birthday”, Amer. Math. Soc. Transl., 225:2 (2008), 55–71 | MR | Zbl

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

[6] I. V. Baibulov, A. M. Budylin, S. B. Levin, Zap. nauchn. semin. POMI, 461, 2017, 14–51

[7] I. V. Baibulov, A. M. Budylin, S. B. Levin, Zap. nauchn. semin. POMI, 471, 2018, 15–37

[8] E. H. Lieb and W. Liniger, Phys. Rev., 130:1963 (1605)

[9] J. B. McGuire, J. Math. Phys., 5:1964, 622 | MR | Zbl

[10] C. N. Yang, Phys. Rev. Lett., 19 (1967), 1312 | DOI | MR | Zbl

[11] W. G. Gibson, S. Y. Larsen, J. Popiel, Phys. Rev. A, 35 (1987), 4919 | DOI

[12] Yu. A. Kuperin, P. B. Kurasov, Yu. B. Melnikov, S. P. Merkuriev, Ann. Phys., 205 (1991), 330 | DOI | MR | Zbl

[13] A. Amaya-Tapia, S. Y. Larsen, J. Popiel, Few-Body Syst., 23 (1998), 87 | DOI

[14] M. Olshanii, Phys. Rev. Lett., 81 (1998), 938 | DOI

[15] Phys. Atom. Nucl., 64 (2001), 27 | DOI | MR

[16] O. Chuluunbaatar, A. A. Gusev, S. Y. Larsen, S. I. Vinitsky, J. Phys. A, 35 (2002), L513 | DOI | MR | Zbl

[17] A. Amaya-Tapia, G. Gasaneo, S. Ovchinnikov, et al., J. Math. Phys., 45 (2004), 3533 | DOI | MR | Zbl

[18] O. I. Tolstikhin C. Namba, Phys. Rev. A, 70 (2004), 062721 | DOI

[19] G. V. Sitnikov O. I. Tolstikhin, Phys. Rev. A, 71 (2005), 022708 | DOI

[20] N. P. Mehta J. R. Shepard, Phys. Rev. A, 72 (2005), 032728 | DOI

[21] O. Chuluunbaatar et al., J. Phys. B, 39 (2006), 243 | DOI

[22] N. P. Mehta, B. D. Esry, C. H. Greene, Phys. Rev. A, 76 (2007), 022711 | DOI

[23] O. Chuluunbaatar et al., Comput. Phys. Commun., 177 (2007), 649 | DOI | MR | Zbl

[24] A. Gorlitz et al., Phys. Rev. Lett., 87 (2001), 130402 | DOI

[25] T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London), 440 (2006), 900 | DOI

[26] T. Kinoshita, T. Wenger, D. S. Weiss, Science, 305 (2004), 1125 | DOI

[27] J. Esteve et al., Phys. Rev. Lett., 96 (2006), 130403 | DOI

[28] A. M. Budylin, S. B. Levin, ZhETF, 162:5 (2022), 657–662

[29] H. Feshbach, C. E. Porter, V. F. Weisskopf, Phys. Rev., II. Ser., 96 (1954), 448–464 | Zbl

[30] A. M. Budylin, V. S. Buslaev, Adv. Sov. Math., 7, Amer. Math. Soc., 1995, 107–157 | MR

[31] F. Calogero, Comm. Math. Phys., 1 (1965), 80 | DOI | MR | Zbl

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

[33] V. S. Buslaev, Ya. Yu. Koptelov, S. B. Levin, D. A. Strygina, Yadernaya Fizika, 76:2 (2013), 236–247 | DOI

[34] B. Simon, Mathematical Surveys and Monographs, 120, Second Edition, American Mathematical Society, 2005 | MR | Zbl