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 — documentation:standard_operators:total_angular_momentum:jsqr [2016/10/10 09:41] (current) 2016/10/06 08:09 Maurits W. Haverkort created 2016/10/06 08:09 Maurits W. Haverkort created 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: + ​ + OppJsqr = NewOperator("​Jsqr",​ NF, IndexUp, IndexDn) + ​ + ### + + + ===== Table of contents ===== + {{indexmenu>​.#​1}}