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 TMF, 1971, Volume 8, Number 2, Pages 235–250 (Mi tmf4401)

Coordinate asymptotic behavior of three-particle wave functions

S. P. Merkur'ev

Abstract: A study is made of the coordfinate asymptotic behavior of the wave function for a system of three nonrelativistic partieles, allowance being made for $(3\to 3)$ processes. Attention is devoted primarily to twofold seattering effects, it is shown that in the parts of the configuration space where the formally constructed scattering amplitude becomes infinite the asymptotic behavior of the $(3\to 3)$ wave function can be described by means of a Fresnel ntegral.

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English version:
Theoretical and Mathematical Physics, 1971, 8:2, 798–809

Citation: S. P. Merkur'ev, “Coordinate asymptotic behavior of three-particle wave functions”, TMF, 8:2 (1971), 235–250; Theoret. and Math. Phys., 8:2 (1971), 798–809

Citation in format AMSBIB
\Bibitem{Mer71} \by S.~P.~Merkur'ev \paper Coordinate asymptotic behavior of three-particle wave functions \jour TMF \yr 1971 \vol 8 \issue 2 \pages 235--250 \mathnet{http://mi.mathnet.ru/tmf4401} \transl \jour Theoret. and Math. Phys. \yr 1971 \vol 8 \issue 2 \pages 798--809 \crossref{https://doi.org/10.1007/BF01038001} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. M. Veselova, “Determination of scattering amplitudes in problems with two and three charged particles”, Theoret. and Math. Phys., 13:3 (1972), 1200–1206
2. S. P. Merkur'ev, “Variational principle for three-particle systems”, Theoret. and Math. Phys., 17:2 (1973), 1105–1111
3. A. I. Baz', S. P. Merkur'ev, “Kinematic properties of three-particle reactions”, Theoret. and Math. Phys., 31:1 (1977), 309–318
4. R. K. Peterkop, L. L. Rabik, “Asymptotic expansions in the problem of three charged particles”, Theoret. and Math. Phys., 31:3 (1977), 502–510
5. S. P. Merkur'ev, “Coordinate asymptotic behavior of $(3\to 3)$ wave functions for a system of three charged particles”, Theoret. and Math. Phys., 32:2 (1977), 680–694
6. E. G. Kolesnichenko, “Kinetic equations for chemically reacting quantum gases. I”, Theoret. and Math. Phys., 30:1 (1977), 73–78
7. B. E. Grinyuk, I. V. Simenog, “Many-particle correlations in an $N$-particle system and many-particle scattering amplitudes”, Theoret. and Math. Phys., 35:1 (1978), 335–345
8. V. E. Kuz'michev, V. F. Kharchenko, “Analytic solution to the problem of three-particle collisions in a model with eikonal Hamiltonian”, Theoret. and Math. Phys., 47:1 (1981), 324–334
9. S. P. Merkur'ev, S. L. Yakovlev, “Quantum $N$-body scattering theory in configuration space”, Theoret. and Math. Phys., 56:1 (1983), 673–682
10. S. L. Yakovlev, “Coordinate asymptotics of the wave function for a system of four particles free in the initial state”, Theoret. and Math. Phys., 82:2 (1990), 157–169
11. Yu. A. Kuperin, Yu. B. Melnikov, “Quantum scattering in gauge fields of adiabatic representations”, Math. USSR-Sb., 72:1 (1992), 221–265
12. Kukulin V.I. Rubtsova O.A., “Modern Approaches for the Theoretical Description of Multiparticle Scattering and Nuclear Reactions”, Phys. Atom. Nuclei, 75:11 (2012), 1373–1387
13. S. L. Yakovlev, “Asymptotic behavior of the wave function of three particles in a continuum”, Theoret. and Math. Phys., 186:1 (2016), 126–135
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