Quanty - documentation:standard_operators:total_angular_momentum
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2026-04-30T14:37:48+00:00Quanty
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https://www.quanty.org/_media/wiki/dokuwiki.svgtext/html2025-11-20T02:29:36+00:00Anonymous (anonymous@undisclosed.example.com)Jmin
https://www.quanty.org/documentation/standard_operators/total_angular_momentum/jmin?rev=1763605776&do=diff
Jmin
The $J^-$ operator is defined as:
\begin{equation}
J^- = L^- + S^-.
\end{equation}
The equivalent operator in Quanty is created by:
OppJmin = NewOperator("Jmin", NF, IndexUp, IndexDn)
Table of contents
total_angular_momentum indextext/html2025-11-20T02:29:37+00:00Anonymous (anonymous@undisclosed.example.com)Jplus
https://www.quanty.org/documentation/standard_operators/total_angular_momentum/jplus?rev=1763605777&do=diff
Jplus
The $J^+$ operator is defined as:
\begin{equation}
J^+ = L^+ + S^+.
\end{equation}
The equivalent operator in Quanty is created by:
OppJplus = NewOperator("Jplus", NF, IndexUp, IndexDn)
Table of contents
total_angular_momentum indextext/html2025-11-20T02:29:37+00:00Anonymous (anonymous@undisclosed.example.com)Jsqr
https://www.quanty.org/documentation/standard_operators/total_angular_momentum/jsqr?rev=1763605777&do=diff
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…text/html2025-11-20T02:29:37+00:00Anonymous (anonymous@undisclosed.example.com)Jx
https://www.quanty.org/documentation/standard_operators/total_angular_momentum/jx?rev=1763605777&do=diff
Jx
The $J_x$ operator is defined as:
\begin{equation}
J_x = L_x + S_x.
\end{equation}
The equivalent operator in Quanty is created by:
OppJx = NewOperator("Jx", NF, IndexUp, IndexDn)
Table of contents
total_angular_momentum indextext/html2025-11-20T02:29:38+00:00Anonymous (anonymous@undisclosed.example.com)Jy
https://www.quanty.org/documentation/standard_operators/total_angular_momentum/jy?rev=1763605778&do=diff
Jy
The $J_y$ operator is defined as:
\begin{equation}
J_y = L_y + S_y.
\end{equation}
The equivalent operator in Quanty is created by:
OppJy = NewOperator("Jy", NF, IndexUp, IndexDn)
Table of contents
total_angular_momentum indextext/html2025-11-20T02:29:37+00:00Anonymous (anonymous@undisclosed.example.com)Jz
https://www.quanty.org/documentation/standard_operators/total_angular_momentum/jz?rev=1763605777&do=diff
Jz
The $J_z$ operator is defined as:
\begin{equation}
J_z = L_z + S_z.
\end{equation}
The equivalent operator in Quanty is created by:
OppJz = NewOperator("Jz", NF, IndexUp, IndexDn)
Table of contents
total_angular_momentum indextext/html2025-11-20T02:29:37+00:00Anonymous (anonymous@undisclosed.example.com)Total angular momentum operators (J)
https://www.quanty.org/documentation/standard_operators/total_angular_momentum/start?rev=1763605777&do=diff
Total angular momentum operators (J)
The total angular momentum $J$ is the sum of the spin and orbital angular momentum $J=S+L$.
Table of contents
total_angular_momentum index