Geodesic
The point interactions in the problem of three quantum particles with internal structure
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 2, pp. 258-282 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of three quantum particles with internal structure is considered where the pair interactions are described in terms of two-channel Hamiltonians. It is proved that if parameters of the model are such that the total three-body Hamiltonian is semibounded, the Faddeev equations are of Fredholm type. The boundary value problems are formulated for the Faddeev differential equations which can be used for search of the scattering wave functions. 
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K. A. Makarov; V. V. Melezhik; A. K. Motovilov. The point interactions in the problem of three quantum particles with internal structure. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 2, pp. 258-282. http://geodesic.mathdoc.fr/item/TMF_1995_102_2_a8/

[1] Fermi E., Ricerca Scientifica, 7 (1936), 13–52

[2] Kronig R. de L., Penney W. G., Proc. Roy. Soc. A (London), 130 (1931), 499–513 | DOI

[3] Bethe H., Peierls R., Proc. Roy. Soc. A (London), 148 (1935), 146–156 | DOI

[4] Berezin F. A., Faddeev L. D., DAN SSSR, 137:5 (1961), 1011–1014 | MR | Zbl

[5] Albeverio S., Gestezi F., Kheeg-Kron R., Kholden Kh., Reshaemye modeli v kvantovoi mekhanike, Mir, M., 1991 | MR

[6] Minlos R. A., Faddeev L. D., DAN SSSR, 141:6 (1961), 1335–1338 | MR

[7] Pavlov B. S., Matem. sb., 136(178):2(6) (1988), 163–177 | MR | Zbl

[8] Skornyakov G. V., Ter-Martirosyan K. A., ZhETF, 31:5 (1956), 775–790 | Zbl

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

[10] Danilov G. S., ZhETF, 40:2 (1961), 498–507 | MR | Zbl

[11] Faddeev L. D., Tr. MIAN SSSR, 69, 1963, 3–122 | MR

[12] Thomas L. H., Phys. Rev., 47 (1935), 903–909 | DOI

[13] Newton R. G., Scattering theory of waves and particles, Springer-Verlag, 1982 | MR | Zbl

[14] Shondin Yu. G., TMF, 51:2 (1982), 181–191 | MR

[15] Thomas L. E., Phys. Rev. D, 30 (1984), 1233–1237 | DOI | MR

[16] Shondin Yu. G., TMF, 74:3 (1988), 331–344 | MR | Zbl

[17] Pavlov B. S., TMF, 59:3 (1984), 345–353 | MR

[18] Pavlov B. S., UMN, 42:6 (1987), 99–131 | MR

[19] Pavlov B. S., Shushkov A. A., Matem. sb., 137(179):2(10) (1988), 147–183 | MR

[20] Motovilov A. K., TMF, 97:2 (1993), 163–181 | MR | Zbl

[21] Makarov K. A., Preprint FUB/HEP–88–3, FUB, Berlin (West), 1988

[22] Makarov K. A., Algebra i analiz, 4:5 (1992), 155–171 | MR

[23] Kuperin Yu. A., Makarov K. A., Merkurev S. P., Motovilov A. K., Pavlov B. S., III Vsesoyuznaya shkola po malochastichnym i kvark-adronnym sistemam, Ch. II, Vilnyus, 1986, 28–73

[24] Kuperin Yu. A., Makarov K. A., Merkurev S. P., Motovilov A. K., Pavlov B. S., TMF, 76:2 (1988), 242–260 | MR

[25] Kuperin Yu. A., Makarov K. A., Merkurev S. P., Motovilov A. K., YaF, 48:2 (1988), 358–371 | MR

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

[27] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR

[28] Merkurev S. P., Motovilov A. K., Yakovlev S. L., TMF, 94:3 (1993), 435–447 | MR

[29] Buslaev V. S., Izv. AN SSSR. Ser. matem., 39 (1975), 149–235 | MR | Zbl

[30] Fedoryuk M. V., Metod perevala, Nauka, M., 1977 | MR

[31] Motovilov A. K., Vestnik LGU, 1983, no. 22, 76–79