## 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.

### MSC:

 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
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### References:

 [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).
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