# Questions tagged [wigner-eckart]

The Wigner–Eckart theorem relates matrix elements of spherical tensor operators in the basis of angular momentum eigenstates to Clebsch–Gordan coefficients. Within a given subspace, a component of such operators behaves proportionally to the same component of the angular momentum operator itself. Do not use for plain Clebsch–Gordan decompositions.

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### Can this matrix be evaluated with the help of the Wigner-Eckart theorem?

I wonder if the problem in the image can be solved with the Wigner-Eckart (W-E) theorem. These elements have to vanish. I tried introducing the identity operator in between $r$ and $p$ to then use the ...
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### Component of a irreducible tensor product

Given the operators $\boldsymbol{\alpha}$ and $\boldsymbol{C^{(L)}}$ such that  \boldsymbol{\alpha}=\left(\begin{array}{cc} 0 & \boldsymbol{\sigma}_{p} \\ \boldsymbol{\sigma}_{p} & 0 \end{...
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### Computing matrix elements using Wigner-Eckart Theorem

I am trying to compute the matrix elements \begin{equation} \langle j \, m | a_{1}^{+} | j' \, m'\rangle \end{equation} \begin{equation} \langle j \, m | a_{2}^{+} | j' \, m'\rangle \end{equation} ...
Working in the $|\alpha, j,m_j\rangle$ basis (denoting all irrelevant quantum numbers by $\alpha$), the Wigner-Eckart theorem tells us that the elements of a rank $k$ spherical tensor $T_q^{(k)}$ can ...