Some integrals involving Coulomb functions associated with the three-dimensional proper Lorentz group

I. A. Shilin; Junesang Choi; Jae Won Lee; I. A. Shilin; Junesang Choi; Jae Won Lee

doi:10.3934/math.2020362

AIMS Mathematics

2020, Volume 5, Issue 6: 5664-5682. doi: 10.3934/math.2020362

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Research article

Some integrals involving Coulomb functions associated with the three-dimensional proper Lorentz group

1.
Department of Higher Mathematics, National Research University MPEI, Krasnokazarmennaya 14, Moscow 111250, Russia
2.
Department of Algebra, Moscow State Pedagogical University, Malaya Pirogovskaya 1, Moscow 119991, Russia
3.
Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea
4.
Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Republic of Korea

Received: 01 May 2020 Accepted: 29 June 2020 Published: 02 July 2020
MSC : 33C10, 33C80, 33B15, 33C05

For two continual bases in the representation space, we obtain the matrix elements of the linear operator transforming the first basis into the second. These elements are expressed in terms of Coulomb wave functions. Computing the matrix elements of subrepresentations to some subgroups or their separate elements and using the connection between above bases, we evaluate some integrals involving Coulomb wave functions.
Citation: I. A. Shilin, Junesang Choi, Jae Won Lee. Some integrals involving Coulomb functions associated with the three-dimensional proper Lorentz group[J]. AIMS Mathematics, 2020, 5(6): 5664-5682. doi: 10.3934/math.2020362

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Abstract

For two continual bases in the representation space, we obtain the matrix elements of the linear operator transforming the first basis into the second. These elements are expressed in terms of Coulomb wave functions. Computing the matrix elements of subrepresentations to some subgroups or their separate elements and using the connection between above bases, we evaluate some integrals involving Coulomb wave functions.

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