V. I. Kukulin, O. A. Rubtsova, “Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)”, TMF, 130:1 (2002), 64–86; Theoret. and Math. Phys., 130:1 (2002), 54

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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 130, Number 1, Pages 64–86
DOI: https://doi.org/10.4213/tmf291 (Mi tmf291)

This article is cited in 15 scientific papers (total in 15 papers)

Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)

V. I. Kukulin, O. A. Rubtsova

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Full-text PDF (334 kB) Citations (15)

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DOI: https://doi.org/10.4213/tmf291

Abstract: Constructing the basic operators of scattering theory on and off the mass shell in terms of spatially bounded stationary wave packets or proper differentials is described. For this, we use a technique based on a certain scheme for discretizing the continuum. Finite-dimensional approximations for the Green's functions and $T$-matrix, which are first found here, are immediately constructed for any energy using a single simple diagonalization of the Hamiltonian matrix in an $L_2$-type complete basis. We show that the developed approach leads to a convenient finite-dimensional representation of the scattering operators in the basis of the wave functions of a harmonic oscillator. The method allows an immediate extension to the problem of three and more bodies.

Received: 23.05.2001

English version:
Theoretical and Mathematical Physics, 2002, Volume 130, Issue 1, Pages 54–73
DOI: https://doi.org/10.1023/A:1013828431342

Bibliographic databases:

Language: Russian

Citation: V. I. Kukulin, O. A. Rubtsova, “Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)”, TMF, 130:1 (2002), 64–86; Theoret. and Math. Phys., 130:1 (2002), 54–73

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf291

https://doi.org/10.4213/tmf291

https://www.mathnet.ru/eng/tmf/v130/i1/p64

This publication is cited in the following 15 articles:

Abdurakhmanov I.B., Kadyrov A.S., Bray I., “Wave-packet continuum-discretization approach to ion-atom collisions: Nonrearrangement scattering”, Phys. Rev. A, 94:2 (2016), 022703
O. A. Rubtsova, V. I. Kukulin, V. N. Pomerantsev, “Quantum scattering theory on the momentum lattice”, Phys. Part. Nuclei, 41:7 (2010), 1123
Pomerantsev, VN, “Solving three-body scattering problems in the momentum lattice representation”, Physical Review C, 79:3 (2009), 034001
Pupyshev, VV, “Generalizations of the Fock and Kato expansions to systems of three quantum particles”, Physics of Particles and Nuclei, 40:4 (2009), 391
JETP Letters, 90:5 (2009), 402–406
Rubtsova, OA, “Quantum scattering theory on the momentum lattice”, Physical Review C, 79:6 (2009), 064602
Rubtsova OA, Kukulin VI, Moro AM, “Continuum discretization methods in a composite particle scattering off a nucleus: Benchmark calculations”, Physical Review C, 78:3 (2008), 034603
V. I. Kukulin, V. N. Pomerantsev, O. A. Rubtsova, “Wave-packet continuum discretization method for solving the three-body scattering problem”, Theoret. and Math. Phys., 150:3 (2007), 403–424
Rubtsova OA, Kukulin VI, “Wave-packet discretization of a continuum: Path toward practically solving few-body scattering problems”, Physics of Atomic Nuclei, 70:12 (2007), 2025–2045
Kukulin VI, Rubtsova OA, “Elastic scattering on a nucleus and the breakup of the composite projectile via wave-packet continuum discretization”, Physical Review C, 76:4 (2007), 047601
The Mathematica GuideBook for Symbolics, 2006, 978
V. I. Kukulin, O. A. Rubtsova, “Solving the Charged-Particle Scattering Problem by Wave Packet Continuum Discretization”, Theoret. and Math. Phys., 145:3 (2005), 1711–1726
V. I. Kukulin, O. A. Rubtsova, “Finite-Dimensional Approximations for Scattering Theory Operators in the Wave-Packet Representation”, Theoret. and Math. Phys., 139:2 (2004), 693–705
V. I. Kukulin, O. A. Rubtsova, “Discrete Quantum Scattering Theory”, Theoret. and Math. Phys., 134:3 (2003), 404–426
Rubtsova O.A., Kukulin V.I., “Efficient technique for solving few-body scattering problems by the wave-packet continuum discretisation”, Few Body Problems in Physics '02, Few-Body Systems Supplementum, 14, 2003, 211–214

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

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