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Citation bot (talk | contribs) Add: s2cid, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Whoop whoop pull up | #UCB_webform 25/27 |
Fixed mistypes in formulas. |
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Line 107:
Y_{K}^{Q}(J) =\sum_{MM^{\prime }}(-1)^{J-M}(2K+1)^{2} \times \left(
\begin{matrix}
J & J & K \\
M^{^{\prime }} \end{matrix}
\right) |JM\rangle \langle JM^{^{\prime }}|,
Line 115:
projection index of rank K which ranges from −K to +K. A cubic harmonic super basis where all the tensor operators are hermitian can be defined as
:<math> T_{K}^{Q} =\frac{1}{\sqrt{2}}[(-1)^{Q}Y_{K}^{Q}(J)+Y_{K}^{-Q}(J)] </math>
:<math> T_{K}^{-Q} =\frac{i}{\sqrt{2}}[Y_{K}^{
Then, any quantum operator <math> A </math> defined in the <math> J </math>-multiplet Hilbert space can be expanded as
:<math> A=\sum_{K,Q}\alpha_{K}^{Q} Y_{K}^{Q}=\sum_{K,Q}\beta_{K}^{Q} T_{K}^{Q}=\sum_{i,j}\gamma_{i,j} L_{i,j} </math>
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