Some aspects of the scattering problem for a system of three charged particles. (English. Russian original) Zbl 1419.81038

J. Math. Sci., New York 238, No. 5, 601-620 (2019); translation from Zap. Nauchn. Semin. POMI 461, 65-94 (2017).
Summary: The question of influence of the spectral neighborhood of an accumulative point of bound energies of a pair subsystem on the structure of eigenfunctions of the continuous spectrum for a system of three charged quantum particles is studied. The unified contribution of pair high-excited states are separated in the coordinate asymptotics of such functions.


81U10 \(n\)-body potential quantum scattering theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35P05 General topics in linear spectral theory for PDEs
70F07 Three-body problems
Full Text: DOI


[1] V. S. Buslaev, S. P. Merkuriev, and S. P. Salikov, “On diffraction character of scattering in quantum system of three one-dimensional particles,” in: Problems of Mathematical Physics, Leningrad University, Leningrad, 9 (1979), pp. 14-30.
[2] Buslaev, VS; Merkuriev, SP; Salikov, SP, Description of pair potentials for which the scattering in the system of three one-dimensional particles is free from diffraction effects, Zap. Nauchn. Semin. LOMI, 84, 16-22, (1979) · Zbl 0413.35058
[3] Buslaev, VS; Levin, SB, Asymptotic behavior of the eigenfunctions of the manyparticle Shrödinger operator. I. One-dimentional Particles, Amer. Math. Soc. Transl., 225, 55-71, (2008)
[4] Buslaev, VS; Levin, SB, Asymptotic behaviour of eigenfunctions of three-body Schrödinger operator. II. Charged one-dimensional particles, Algebra Analiz, 22, 60-79, (2010)
[5] Buslaev, VS; Levin, SB, A system of three three-dimensional charged quantum particles: asymptotic behavior of the eigenfunctions of the continuous spectrum at infinity, Funct. Analiz Prilozh., 46, 83-89, (2012) · Zbl 1272.81185
[6] Koptelov, YY; Levin, SB, On the asymptotic behavior in the scattering problem for several charged quantum particles interacting via repulsive pair potentials, Physics of Atomic Nuclei, 77, 528-536, (2014)
[7] A. M. Budylin, Ya. Yu. Koptelov, and S. B. Levin, “On continuous spectrum eigenfunctions asymptotics of three three-dimensional unlike-charged quantum particles scattering problem,” in: Proceedings of the International Conference, Days on Diffraction, Retersburg (2016), pp. 89-94.
[8] Levin, SB, On the asymptotic behaviour of eigenfunctions of the continuous spectrum at infinity in configuration space for the system of three three-dimensional like-charged particles, J. Math. Sci., 226, 744-768, (2017) · Zbl 1380.81121
[9] Alt, EO; Mukhamedzhanov, AM, Asymptotic solution of the Schrödinger equation for three charged particles, JETP Lett., 56, 435-438, (1992)
[10] Alt, EO; Mukhamedzhanov, AM, Asymptotic solution of the Schrödinger equation for three charged particles, Phys. Rev. A, 47, 2004-2022, (1993)
[11] Brauner, M.; Briggs, JS; Klar, H., Triply-differential cross sections for ionisation of hydrogen atoms by electrons and positrons, J. Phys. B, 22, 2265-2287, (1989)
[12] S. P. Merkuriev and L. D. Faddeev, Quantum Scattering Theory For Several Particle Systems, Kluwer, Dordrecht (1993). · Zbl 0797.47005
[13] Garibotti, G.; Miraglia, JE, Ionization and electron capture to the continuum in the H+-hydrogen-atom collision, Phys. Rev. A, 21, 572-580, (1980)
[14] A. L. Godunov, Sh. D. Kunikeev, V. N. Mileev, and V. S. Senashenko, in: Proceedings of the 13th International Conference on Physics of Electronic and Atomic collisions (Berlin), ed. J. Eichler (Amsterdam: North Holland), Abstracts (1983), p. 380.
[15] L. D. Faddeev, Mathematical Aspects of the Three-Body Problem of the Quantum Scattering Theory, Daniel Davey and Co., Inc.,Jerusalem (1965). · Zbl 0131.43504
[16] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, San Diego (1980). · Zbl 0521.33001
[17] L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Vol. 3 of A Course of Theoretical Physics, Pergamon Press (1965).
[18] N. McLachlan, Theory and Application of Mathieu Functions, Oxford (1947).
[19] Tricomi, F., Sul comportamento asintotico dei polinomi di Laguerre, Ann. Mat. Pura Appl., 28, 263-289, (1949) · Zbl 0039.29903
[20] I. M. Gelfand and G. E. Shilov, Generalized Functions and Operations With Them [in Russian], Fiz.-Mat. Lit., Moscow (1958).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.