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Closed form representation for a projection onto infinitely-dimensional subspace spanned by Coulomb bound states. / Deryuzhkova, O. M.; Levin, S. B.; Yakovlev, S. L.

In: Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 39, No. 22, 019, 28.11.2006, p. 4767-4773.

Research output: Contribution to journal › Article › peer-review

Harvard

Deryuzhkova, OM, Levin, SB & Yakovlev, SL 2006, 'Closed form representation for a projection onto infinitely-dimensional subspace spanned by Coulomb bound states', Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 39, no. 22, 019, pp. 4767-4773. https://doi.org/10.1088/0953-4075/39/22/019

APA

Deryuzhkova, O. M., Levin, S. B., & Yakovlev, S. L. (2006). Closed form representation for a projection onto infinitely-dimensional subspace spanned by Coulomb bound states. Journal of Physics B: Atomic, Molecular and Optical Physics, 39(22), 4767-4773. [019]. https://doi.org/10.1088/0953-4075/39/22/019

Vancouver

Deryuzhkova OM, Levin SB, Yakovlev SL. Closed form representation for a projection onto infinitely-dimensional subspace spanned by Coulomb bound states. Journal of Physics B: Atomic, Molecular and Optical Physics. 2006 Nov 28;39(22):4767-4773. 019. https://doi.org/10.1088/0953-4075/39/22/019

Author

Deryuzhkova, O. M. ; Levin, S. B. ; Yakovlev, S. L. / Closed form representation for a projection onto infinitely-dimensional subspace spanned by Coulomb bound states. In: Journal of Physics B: Atomic, Molecular and Optical Physics. 2006 ; Vol. 39, No. 22. pp. 4767-4773.

BibTeX

@article{435f379e08ad433fb418626c8e8ab027,
title = "Closed form representation for a projection onto infinitely-dimensional subspace spanned by Coulomb bound states",
abstract = "The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the n2-dimensional subspace corresponding to the nth eigenvalue in the Coulomb discrete spectrum is also represented as the combination of Laguerre polynomials of nth and (n - 1)th order. The latter allows us to derive an analogue of the Christoffel-Darboux summation formula for the Laguerre polynomials. The representations obtained are believed to be helpful in solving the breakup problem in a system of three charged particles where the correct treatment of infinitely many bound states in two-body subsystems is one of the most difficult technical problems.",
author = "Deryuzhkova, {O. M.} and Levin, {S. B.} and Yakovlev, {S. L.}",
year = "2006",
month = nov,
day = "28",
doi = "10.1088/0953-4075/39/22/019",
language = "English",
volume = "39",
pages = "4767--4773",
journal = "Journal of the European Optical Society Part B: Quantum Optics",
issn = "0953-4075",
publisher = "IOP Publishing Ltd.",
number = "22",

}

RIS

TY - JOUR

T1 - Closed form representation for a projection onto infinitely-dimensional subspace spanned by Coulomb bound states

AU - Deryuzhkova, O. M.

AU - Levin, S. B.

AU - Yakovlev, S. L.

PY - 2006/11/28

Y1 - 2006/11/28

N2 - The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the n2-dimensional subspace corresponding to the nth eigenvalue in the Coulomb discrete spectrum is also represented as the combination of Laguerre polynomials of nth and (n - 1)th order. The latter allows us to derive an analogue of the Christoffel-Darboux summation formula for the Laguerre polynomials. The representations obtained are believed to be helpful in solving the breakup problem in a system of three charged particles where the correct treatment of infinitely many bound states in two-body subsystems is one of the most difficult technical problems.

AB - The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the n2-dimensional subspace corresponding to the nth eigenvalue in the Coulomb discrete spectrum is also represented as the combination of Laguerre polynomials of nth and (n - 1)th order. The latter allows us to derive an analogue of the Christoffel-Darboux summation formula for the Laguerre polynomials. The representations obtained are believed to be helpful in solving the breakup problem in a system of three charged particles where the correct treatment of infinitely many bound states in two-body subsystems is one of the most difficult technical problems.

UR - http://www.scopus.com/inward/record.url?scp=33846043130&partnerID=8YFLogxK

U2 - 10.1088/0953-4075/39/22/019

DO - 10.1088/0953-4075/39/22/019

M3 - Article

VL - 39

SP - 4767

EP - 4773

JO - Journal of the European Optical Society Part B: Quantum Optics

JF - Journal of the European Optical Society Part B: Quantum Optics

SN - 0953-4075

IS - 22

M1 - 019

ER -

ID: 5076033