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TMF, 2003, Volume 134, Number 3, Pages 460–486 (Mi tmf165)  

This article is cited in 13 scientific papers (total in 13 papers)

Discrete Quantum Scattering Theory

V. I. Kukulin, O. A. Rubtsova

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: We formulate quantum scattering theory in terms of a discrete $L_2$-basis of eigen differentials. Using projection operators in the Hilbert space, we develop a universal method for constructing finite-dimensional analogues of the basic operators of the scattering theory: $S$- and $T$-matrices, resolvent operators, and Möller wave operators as well as the analogues of resolvent identities and the Lippmann–Schwinger equations for the $T$-matrix. The developed general formalism of the discrete scattering theory results in a very simple calculation scheme for a broad class of interaction operators.

Keywords: quantum scattering theory, wave packets, Green's function, wave operator, $T$-matrix, discretization of continuum

DOI: https://doi.org/10.4213/tmf165

Full text: PDF file (371 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 134:3, 404–426

Bibliographic databases:

Received: 11.03.2002

Citation: V. I. Kukulin, O. A. Rubtsova, “Discrete Quantum Scattering Theory”, TMF, 134:3 (2003), 460–486; Theoret. and Math. Phys., 134:3 (2003), 404–426

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\vol 134
\issue 3
\pages 404--426
\crossref{https://doi.org/10.1023/A:1022657607306}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Nunes FM, Mukhamedzhanov AM, Rosa CC, et al, “Insight into continuum couplings”, Nuclear Physics A, 736:3–4 (2004), 255–268  crossref  adsnasa  isi  scopus  scopus
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. 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  crossref  adsnasa  isi  scopus  scopus
    6. 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  crossref  adsnasa  isi  elib  scopus  scopus
    7. 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  crossref  adsnasa  isi  elib  scopus  scopus
    8. Pupyshev, VV, “Generalizations of the Fock and Kato expansions to systems of three quantum particles”, Physics of Particles and Nuclei, 40:4 (2009), 391  crossref  adsnasa  isi  scopus  scopus
    9. JETP Letters, 90:5 (2009), 402–406  mathnet  crossref  isi  elib
    10. Rubtsova, OA, “Quantum scattering theory on the momentum lattice”, Physical Review C, 79:6 (2009), 064602  crossref  adsnasa  isi
    11. Pomerantsev V.N., Kukulin V.I., Rubtsova O.A., “Solving three-body scattering problems in the momentum lattice representation”, Physical Review C, 79:3 (2009), 034001  crossref  adsnasa  isi  elib  scopus  scopus
    12. Kelvich S.A., Kukulin V.I., Rubtsova O.A., “Path Toward Fast Calculations in Quantum Scattering Theory”, Phys. Atom. Nuclei, 77:4 (2014), 438–445  crossref  adsnasa  isi  scopus  scopus
    13. Rubtsova O.A. Kukulin V.I. Pomerantsev V.N., “Wave-Packet Continuum Discretization For Quantum Scattering”, Ann. Phys., 360 (2015), 613–654  crossref  mathscinet  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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