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documentation:standard_operators:total_angular_momentum:jsqr [2016/10/10 09:41] (current)
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 +====== 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}}
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