Geodesic
A System of Three Three-Dimensional Charged Quantum Particles: Asymptotic Behavior of the Eigenfunctions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 83-88.

Voir la notice de l'article provenant de la source Math-Net.Ru

To our knowledge, there are no expressions (not necessarily rigorously proved mathematically) for the eigenfunctions of a system of three or more charged quantum particles. For a system of three such identical particles, we suggest an asymptotic formula describing the behavior of eigenfunctions at infinity in the configuration space.
Keywords: partial differential equations, mathematical physics, quantum scattering theory in the system of three charged particles. 
@article{FAA_2012_46_2_a7,
     author = {V. S. Buslaev and S. B. Levin},
     title = {A {System} of {Three} {Three-Dimensional} {Charged} {Quantum} {Particles:} {Asymptotic} {Behavior} of the {Eigenfunctions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {83--88},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a7/}
}
TY  - JOUR
AU  - V. S. Buslaev
AU  - S. B. Levin
TI  - A System of Three Three-Dimensional Charged Quantum Particles: Asymptotic Behavior of the Eigenfunctions
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2012
SP  - 83
EP  - 88
VL  - 46
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a7/
LA  - ru
ID  - FAA_2012_46_2_a7
ER  - 
%0 Journal Article
%A V. S. Buslaev
%A S. B. Levin
%T A System of Three Three-Dimensional Charged Quantum Particles: Asymptotic Behavior of the Eigenfunctions
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2012
%P 83-88
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a7/
%G ru
%F FAA_2012_46_2_a7
V. S. Buslaev; S. B. Levin. A System of Three Three-Dimensional Charged Quantum Particles: Asymptotic Behavior of the Eigenfunctions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 83-88. http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a7/

[1] L. D. Faddeev, “Matematicheskie voprosy kvantovoi teorii rasseyaniya dlya sistemy trekh chastits”, Trudy MIAN SSSR, 69, Izd-vo AN SSSR, M., 1963 | MR

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

[3] V. S. Buslaev, S. B. Levin, P. Neittaannmäki, T. Ojala, J. Phys. A: Math. Theor., 43:28 (2010), Article ID 285205 | DOI | MR | Zbl

[4] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1963 | MR

[5] V. S. Buslaev, Problemy matematicheskoi fiziki, t. 1. Spektralnaya teoriya i volnovye protsessy, Izd-vo Leningrad. un-ta, 1966, 82–101 | MR

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

[7] C. R. Garibotti, J. E. Miraglia, Phys. Rev. A, 21:2 (1980), 572–580 | DOI

[8] A. L. Godunov, Sh. D. Kunikeev, V. N. Mileev, V. S. Senashenko, Proc. 13th Int. Conf. on Physics of Electronic and Atomic Collisions (Berlin), North Holland, Amsterdam, 1983, Abstracts, p. 380

[9] E. O. Alt, A. M. Mukhamedzhanov, Pisma v ZhETF, 56:9 (1992), 450–454 | MR