Geodesic
Three-body problems with $\delta$-functional potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 2, pp. 181-191 
Yu. G. Shondin. Three-body problems with $\delta$-functional potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 2, pp. 181-191. http://geodesic.mathdoc.fr/item/TMF_1982_51_2_a3/
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     author = {Yu. G. Shondin},
     title = {Three-body problems with $\delta$-functional potentials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {181--191},
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     volume = {51},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_51_2_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Possible realizations of three-particle singular Hamiltonians corresponding to $\delta$-functional two-body potentials are described. The scheme used to describe the singular potentials is essentially the same as Shirokov's [1, 2]. It is shown that besides the classical model [3, 4] it is possible to have other sensible realizations which go beyond the space of square integrable functions but still have a semibounded Hamiltonian.

[1] Shirokov Yu. M., TMF, 40:3 (1979), 348–354 | MR | Zbl

[2] Shirokov Yu. M., TMF, 42:1 (1980), 45–49 | MR

[3] Skornyakov G. V., Ter-Martirosyan K. A., ZhETF, 31:5 (1956), 775–790 ; Данилов Г. С., ЖЭТФ, 40:2 (1961), 498–507 | Zbl | MR | Zbl

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

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

[6] Albeverio S., Høegh-Krohn R,, Streit L., J. Math. Phys., 18:5 (1977), 907–917 | DOI | MR | Zbl

[7] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, t. 2, Mir, M., 1978 | MR

[8] Khepp K., Teoriya perenormirovok, Nauka, M., 1974 | MR

[9] Kato T., J. Funct. Analysis, 1967, no. 1, 342–369 | DOI | MR | Zbl