Symbolic Algorithm for Generating the Orthonormal Bargmann–Moshinsky Basis for \(\mathrm {SU(3)}\) Group

  • A. Deveikis
  • A. A. Gusev
  • V. P. Gerdt
  • S. I. VinitskyEmail author
  • A. Góźdź
  • A. Pȩdrak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11077)


A symbolic algorithm which can be implemented in any computer algebra system for generating the Bargmann–Moshinsky (BM) basis with the highest weight vectors of \(\mathrm {SO(3)}\) irreducible representations is presented. The effective method resulting in analytical formula of overlap integrals in the case of the non-canonical BM basis [S. Alisauskas, P. Raychev, R. Roussev, J. Phys. G 7, 1213 (1981)] is used. A symbolic recursive algorithm for orthonormalisation of the obtained basis is developed. The effectiveness of the algorithms implemented in Mathematica 10.1 is investigated by calculation of the overlap integrals for up to \(\mu =5\) with \(\lambda > \mu \) and orthonormalization of the basis for up to \(\mu =4\) with \(\lambda > \mu \). The action of the zero component of the quadrupole operator onto the basis vectors with \(\mu =4\) is also obtained.


SU(3) non-canonical basis Group theory Gram-Schmidt orthonormalization Symbolic algorithms 



The work was partially funded by the RFBR grant No. 16-01-00080, the Bogoliubov–Infeld program, and the RUDN University Program 5-100.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • A. Deveikis
    • 1
  • A. A. Gusev
    • 2
  • V. P. Gerdt
    • 2
    • 3
  • S. I. Vinitsky
    • 2
    • 3
    Email author
  • A. Góźdź
    • 4
  • A. Pȩdrak
    • 5
  1. 1.Department of Applied InformaticsVytautas Magnus UniversityKaunasLithuania
  2. 2.Joint Institute for Nuclear ResearchDubnaRussia
  3. 3.RUDN UniversityMoscowRussia
  4. 4.Institute of PhysicsMaria Curie-Skłodowska UniversityLublinPoland
  5. 5.National Centre for Nuclear ResearchWarsawPoland

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