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--- documentation:standard_operators:total_angular_momentum:jsqr [2016/10/06 08:09] – created Maurits W. Haverkort
+++ documentation:standard_operators:total_angular_momentum:jsqr [2025/11/20 03:29] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+====== Jsqr ======
+###
+The $J^2$ operator is defined as:
+\begin{eqnarray}
+J^2 = \sum_{m=-l}^{m=l}\sum_{\sigma} && \left(\frac{3}{4}+l(l+1)+2m\sigma\right) a^{\dagger}_{m,\sigma}a^{\phantom{\dagger}}_{m,\sigma}\\
+\nonumber +\sum_{m=-l}^{m=l}&& \sqrt{l+m+1}\sqrt{l-m} \times \, (a^{\dagger}_{m+1,\downarrow}a^{\phantom{\dagger}}_{m,\uparrow}+a^{\dagger}_{m,\uparrow}a^{\phantom{\dagger}}_{m+1,\downarrow})\\
+\nonumber +\sum_{m_1,m_2=-l}^{m_1,m_2=l}\sum_{\sigma_1,\sigma_2} && \bigg( -(m_1m_2+\sigma_1\sigma_2+m_1\sigma_2) \,  a^{\dagger}_{m_1,\sigma_1}a^{\dagger}_{m_2,\sigma_2}a^{\phantom{\dagger}}_{m_1,\sigma_1}a^{\phantom{\dagger}}_{m_2,\sigma_2}\\
+\nonumber &&\quad -\sqrt{l+m_1+1}\sqrt{l-m_1}\sqrt{l+m_2+1}\sqrt{l-m_2}\\
+\nonumber &&\quad \times \, a^{\dagger}_{m_1+1,\sigma_1}a^{\dagger}_{m_2,\sigma_2}a^{\phantom{\dagger}}_{m_1,\sigma_1}a^{\phantom{\dagger}}_{m_2+1,\sigma_2} \bigg).
+\end{eqnarray}
+The equivalent operator in Quanty is created by:
+<code Quanty Example.Quanty>
+OppJsqr = NewOperator("Jsqr", NF, IndexUp, IndexDn)
+</code>
+###
+===== Table of contents =====
+{{indexmenu>.#1}}