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Wigner-Eckart Theorem

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Angular Momentum Theory Applied to Interactions in Solids

Part of the book series: Lecture Notes in Chemistry ((LNC,volume 47))

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Abstract

The Wigner-Eckart theorem states that if we have a spherical tensor Tkq in the space spanned by the wave functions |JM>, then the matrix elements are

$$<J'M'\left| {{T_{kq}}} \right|JM>=<J(M)k(q)\left| {J'(M')>\;<J'\left| {{T_k}} \right|J>\quad (Rose,\;1957)\;or\;<J'M'\left| {{T_{kq}}} \right|JM>= {{( - 1)}^{J' - M'}}(\begin{array}{*{20}{c}}{L'} & k & L \\{ - M'} & q & M \\\end{array} )(J'\left| {{T_k}} \right|J)\quad (Judd,\quad 1963;\;Wybourne,\;1965).} \right.$$
((3.1))

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Annotated Bibliography and References

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Authors and Affiliations

  1. Harry Diamond Laboratories, 2800 Powder Mill Road, Adelphi, MD, 20783, USA

    C. A. Morrison

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  1. C. A. Morrison
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© 1988 Springer-Verlag Berlin Heidelberg

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Morrison, C.A. (1988). Wigner-Eckart Theorem. In: Angular Momentum Theory Applied to Interactions in Solids. Lecture Notes in Chemistry, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93376-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-93376-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18990-9

  • Online ISBN: 978-3-642-93376-9

  • eBook Packages: Springer Book Archive

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