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documentation:standard_operators:crystal_field [2024/10/03 18:07] – Maurits W. Haverkortdocumentation:standard_operators:crystal_field [2024/10/03 18:07] (current) – Maurits W. Haverkort
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 A_{k,m}        &= \frac{1}{\sqrt{(k-m)!}}\frac{1}{\sqrt{(k+m)!}} \\  A_{k,m}        &= \frac{1}{\sqrt{(k-m)!}}\frac{1}{\sqrt{(k+m)!}} \\ 
 \nonumber &\times \big\langle R_{n_1,l_1}(r) \big| \\ \nonumber &\times \big\langle R_{n_1,l_1}(r) \big| \\
-\nonumber &\quad \partial_z^{l-|m|}(-\rm{Sign}[m]\partial_x+\imath\partial_y)^{|m|}V(r,\theta,\phi)\big|_{r=0} \\+\nonumber &\quad \partial_z^{k-|m|}(-\rm{Sign}[m]\partial_x+\imath\partial_y)^{|m|}V(r,\theta,\phi)\big|_{r=0} \\
 \nonumber & \quad\quad\quad \big| R_{n_2,l_2}(r) \big\rangle. \nonumber & \quad\quad\quad \big| R_{n_2,l_2}(r) \big\rangle.
 \end{align} \end{align}

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