Theoretica chimica acta

, Volume 32, Issue 1, pp 27–40 | Cite as

Symmetry coupling coefficients for point groups and the importance of Racah's Lemma for the standardization of phase

  • Edgar König
  • Stefan Kremer


Useful approaches to the calculation of symmetry coupling coefficients 〈Г1 γ1Г2/2|Гγb〉 are reviewed. Since a common phase factor always remains undetermined for each trio ofГ1,Г2, andГ, a unique standardization of phase is proposed by the requirement, in Racah's lemma, (j1Г1a1,j2Г2a2|j Г ab) ≧ 0and real. In conjunction with the basis relations and the phase convention for Wigner coefficients, a novel method is suggested for the calculation of symmetry coupling coefficients in the group G from those in the subgroupGSU(2) orR3. The results apply in full generality to any point groupG, single or double group.

Key words

Coupling coefficients Lemma of Racah Phase standardization 


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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Edgar König
    • 1
  • Stefan Kremer
    • 1
  1. 1.Institute of Physical Chemistry IIUniversity of Erlangen-NürnbergErlangenGermany

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