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TMF, 2002, Volume 130, Number 1, Pages 64–86 (Mi tmf291)  

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

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.


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English version:
Theoretical and Mathematical Physics, 2002, 130:1, 54–73

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Received: 23.05.2001

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
\by V.~I.~Kukulin, O.~A.~Rubtsova
\paper Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)
\jour TMF
\yr 2002
\vol 130
\issue 1
\pages 64--86
\jour Theoret. and Math. Phys.
\yr 2002
\vol 130
\issue 1
\pages 54--73

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    This publication is cited in the following articles:
    1. V. I. Kukulin, O. A. Rubtsova, “Discrete Quantum Scattering Theory”, Theoret. and Math. Phys., 134:3 (2003), 404–426  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. 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  crossref  isi
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. 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
    9. Pomerantsev, VN, “Solving three-body scattering problems in the momentum lattice representation”, Physical Review C, 79:3 (2009), 034001  crossref  adsnasa  isi  elib  scopus  scopus
    10. 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
    11. JETP Letters, 90:5 (2009), 402–406  mathnet  crossref  isi  elib
    12. Rubtsova, OA, “Quantum scattering theory on the momentum lattice”, Physical Review C, 79:6 (2009), 064602  crossref  adsnasa  isi
    13. 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  crossref  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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