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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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[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. · Zbl 0494.47010
[2] V. S. Buslaev, S. P. Merkuriev, and S. P. Salikov, “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] V. S. Buslaev and S. B. Levin, “Asymptotic behavior of the eigenfunctions of the manyparticle Shrödinger operator. I. One-dimentional Particles,” Amer. Math. Soc. Transl., 225, 55-71 (2008).
[4] V. S. Buslaev and S. B. Levin, “Asymptotic behaviour of eigenfunctions of three-body Schrödinger operator. II. Charged one-dimensional particles,” Algebra Analiz, 22(3), 60-79 (2010).
[5] V. S. Buslaev and S. B. Levin, “A system of three three-dimensional charged quantum particles: asymptotic behavior of the eigenfunctions of the continuous spectrum at infinity,” Funct. Analiz Prilozh., 46, No. 2, 83-89 (2012). · Zbl 1272.81185 · doi:10.4213/faa3067
[6] Ya. Yu. Koptelov and S. B. Levin, “On the asymptotic behavior in the scattering problem for several charged quantum particles interacting via repulsive pair potentials,” Physics of Atomic Nuclei, 77(4), 528-536 (2014). · doi:10.1134/S1063778814040036
[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] S. B. Levin, “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(6), 744-768 (2017). · Zbl 1380.81121 · doi:10.1007/s10958-017-3564-4
[9] E. O. Alt and A. M. Mukhamedzhanov, “Asymptotic solution of the Schrödinger equation for three charged particles,” JETP Lett., 56, No. 9, 435-438 (1992).
[10] E. O. Alt and A. M. Mukhamedzhanov, “Asymptotic solution of the Schrödinger equation for three charged particles,” Phys. Rev. A, 47, No. 3, 2004-2022 (1993). · doi:10.1103/PhysRevA.47.2004
[11] M. Brauner, J. S. Briggs, and H. Klar, “Triply-differential cross sections for ionisation of hydrogen atoms by electrons and positrons,” J. Phys. B, 22, 2265-2287 (1989). · doi:10.1088/0953-4075/22/14/010
[12] S. P. Merkuriev and L. D. Faddeev, Quantum Scattering Theory For Several Particle Systems, Kluwer, Dordrecht (1993). · Zbl 0797.47005
[13] G. Garibotti and J. E. Miraglia, “Ionization and electron capture to the continuum in the H+-hydrogen-atom collision,” Phys. Rev. A, 21(2), 572-580 (1980). · doi:10.1103/PhysRevA.21.572
[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). · Zbl 0029.02901
[19] F. Tricomi, “Sul comportamento asintotico dei polinomi di Laguerre,” Ann. Mat. Pura Appl.(4), 28, 263-289 (1949). · Zbl 0039.29903 · doi:10.1007/BF02411134
[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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