The Transformation of Irreducible Tensor Operators Under Spherical Functions
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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.
KeywordsIrreducible tensor operator Rotation matrix Spherical function Matrix element
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- 1.Condon, E.U., Shortley, G.H.: The Theory of Atomic Spectra. Cambridge Univ. Press, Cambridge (1935) Google Scholar
- 2.Jucys, A.P., Savukynas, A.J.: Mathematical Foundations of the Atomic Theory. Mokslas Publishers, Vilnius (1973) (in Russian) Google Scholar
- 6.Fano, U., Racah, G.: Irreducible Tensor Sets. Academic Press, New York (1959) Google Scholar
- 10.Jucys, A.P., Bandzaitis, A.A.: Theory of angular momentum in quantum mechanics, 2nd edn, Mokslas Publishers, Vilnius (1977) (in Russian) Google Scholar