International Journal of Theoretical Physics

, Volume 49, Issue 9, pp 2230–2245 | Cite as

The Transformation of Irreducible Tensor Operators Under Spherical Functions

  • Rytis Juršėnas
  • Gintaras Merkelis


The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the spherical coordinates of vector in the fixed and rotated coordinate systems are determined. A new way of calculation of the irreducible coupled tensor product matrix elements is suggested. As an example, the proposed technique is applied for the matrix element construction for two electrons in a field of a fixed nucleus.


Irreducible tensor operator Rotation matrix Spherical function Matrix element 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Theoretical Physics and AstronomyVilnius UniversityVilniusLithuania

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