Geodesic
The scattering problem of three one-dimensional quantum particles. The case of pair Coulomb potentials of repulsion at large distances
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 88-101 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the present work the quantum scattering problem for three one-dimensional particles with pair potenrials of Coulomb repulsion at large distances is considered. The coordinate asymptotics of the resolvent kernel in the so called BBK-domain is calculated, it making possible a reduction to the already solved scattering problem with short-range potentials. On the basis of the reduction the coordinate asymptotics resolvent kernel in all configuration space is constructed, with the spectral parameter sitting on the absolutely continuous spectrum. The formulas obtained allow to strictly justify the coordinate asymptotics of the absolutely continuous spectrum wave functions received in frames of the diffraction approach. 
@article{ZNSL_2020_493_a6,
     author = {A. M. Budylin and S. B. Levin},
     title = {The scattering problem of three one-dimensional quantum particles. {The} case of pair {Coulomb} potentials of repulsion at large distances},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--101},
     year = {2020},
     volume = {493},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a6/}
}
TY  - JOUR
AU  - A. M. Budylin
AU  - S. B. Levin
TI  - The scattering problem of three one-dimensional quantum particles. The case of pair Coulomb potentials of repulsion at large distances
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 88
EP  - 101
VL  - 493
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a6/
LA  - ru
ID  - ZNSL_2020_493_a6
ER  - 
%0 Journal Article
%A A. M. Budylin
%A S. B. Levin
%T The scattering problem of three one-dimensional quantum particles. The case of pair Coulomb potentials of repulsion at large distances
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 88-101
%V 493
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a6/
%G ru
%F ZNSL_2020_493_a6
A. M. Budylin; S. B. Levin. The scattering problem of three one-dimensional quantum particles. The case of pair Coulomb potentials of repulsion at large distances. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 88-101. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a6/

[1] I. V. Baibulov, A. M. Budylin, S. B. Levin, “Zadacha rasseyaniya neskolkikh odnomernykh kvantovykh chastits. Struktura i asimptotika predelnykh znachenii yadra rezolventy”, Zap. nauchn. sem. POMI, 461, 2017, 14–51

[2] V. S. Buslaev, S. P. Merkurev, S. P. Salikov, “O difraktsionnom kharaktere rasseyaniya v kvantovoi sisteme trekh odnomernykh chastits”, Problemy matem. fiziki, 9 (1979), 14–30 | Zbl

[3] V. S. Buslaev, S. P. Merkurev, S. P. Salikov, “Opisanie parnykh potentsialov, dlya kotorykh rasseyanie v sisteme trekh odnomernykh chastits svobodno ot difraktsionnykh effektov”, Granichnye zadachi matematicheskoi fiziki i smezhnye voprosy v teorii funktsii, Zap. nauchn. sem. LOMI, 11, 1979, 16–22

[4] V. S. Buslaev, S. B. Levin, “Asymptotic behavior of the eigenfunctions of many-particle Schrödinger operator. I. One-dimensional particles”, Selected topics in mathematical physics, Amer. Math. Soc.Transl. (2), 225, 2008, 55–71 | DOI | MR | Zbl

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

[6] R. Kurant, Uravneniya s chastnymi proizvodnymi, Mir, M., 1964

[7] V. S. Buslaev, S. B. Levin, “Asimptoticheskoe povedenie sobstvennykh funktsii trekhchastichnogo operatora Shredingera. II Odnomernye zaryazhennye chastitsy”, Algebra i analiz, 22:3 (2010), 60–79