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--- physics_chemistry:point_groups:c6:orientation_z [2018/04/06 09:09] – Maurits W. Haverkort
+++ physics_chemistry:point_groups:c6:orientation_z [2024/06/27 09:19] (current) – Typo: indices m and l were switched in spherical harmonics in "we can express the operator as ..." Finn Keuchel
@@ Line 164: / Line 164: @@
 we can express the operator as
-$$ O = \sum_{n'',l'',m'',n',l',m',k,m} A_{n''l'',n'l'}(k,m) \left\langle Y_{l''}^{(m'')}(\theta,\phi) \left| C_{k}^{(m)}(\theta,\phi) \right| Y_{l'}^{(m')}(\theta,\phi) \right\rangle a^{\dagger}_{n'',l'',m''}a^{\phantom{\dagger}}_{n',l',m'}$$
+$$ O = \sum_{n'',l'',m'',n',l',m',k,m} A_{n''l'',n'l'}(k,m) \left\langle Y_{m''}^{(l'')}(\theta,\phi) \left| C_{k}^{(m)}(\theta,\phi) \right| Y_{m'}^{(l')}(\theta,\phi) \right\rangle a^{\dagger}_{n'',l'',m''}a^{\phantom{\dagger}}_{n',l',m'}$$