Quanty - documentation:standard_operators:charge_quadrupole
https://www.quanty.org/
2026-04-15T00:39:59+00:00Quanty
https://www.quanty.org/
https://www.quanty.org/_media/wiki/dokuwiki.svgtext/html2025-11-20T02:29:36+00:00Anonymous (anonymous@undisclosed.example.com)Qxx
https://www.quanty.org/documentation/standard_operators/charge_quadrupole/qxx?rev=1763605776&do=diff
Qxx
The xx component of $Q$ is defined as:
\begin{equation}
Q_{xx} = 3x^2/r^2 - 1.
\end{equation}
The equivalent operator in Quanty is created by:
OppQxx = NewOperator("Qxx", NF, IndexUp, IndexDn)
The operator could also be defined by:
Akm={{2,-2,sqrt(1.5)},{2, 2,sqrt(1.5)},{2,0,-1}}
OppQxx=NewOperator("CF",NF,indexup,indexdn,Akm)
charge_quadrupole indextext/html2025-11-20T02:29:36+00:00Anonymous (anonymous@undisclosed.example.com)Qxy
https://www.quanty.org/documentation/standard_operators/charge_quadrupole/qxy?rev=1763605776&do=diff
Qxy
The xy component of $Q$ is defined as:
\begin{equation}
Q_{xy} = 3xy/r^2.
\end{equation}
The equivalent operator in Quanty is created by:
OppQxy = NewOperator("Qxy", NF, IndexUp, IndexDn)
The operator could also be defined by:
Akm={{2,-2,sqrt(1.5)*I},{2, 2,-sqrt(1.5)*I}}
OppQxy=NewOperator("CF",NF,indexup,indexdn,Akm)
charge_quadrupole indextext/html2025-11-20T02:29:36+00:00Anonymous (anonymous@undisclosed.example.com)Qxz
https://www.quanty.org/documentation/standard_operators/charge_quadrupole/qxz?rev=1763605776&do=diff
Qxz
The xz component of $Q$ is defined as:
\begin{equation}
Q_{xz} = 3xz/r^2.
\end{equation}
The equivalent operator in Quanty is created by:
OppQxz = NewOperator("Qxz", NF, IndexUp, IndexDn)
The operator could also be defined by:
Akm={{2,-1,sqrt(1.5) },{2, 1,-sqrt(1.5) }}
OppQxz=NewOperator("CF",NF,indexup,indexdn,Akm)
charge_quadrupole indextext/html2025-11-20T02:29:35+00:00Anonymous (anonymous@undisclosed.example.com)Qyy
https://www.quanty.org/documentation/standard_operators/charge_quadrupole/qyy?rev=1763605775&do=diff
Qyy
The yy component of $Q$ is defined as:
\begin{equation}
Q_{yy} = 3y^2/r^2 - 1.
\end{equation}
The equivalent operator in Quanty is created by:
OppQyy = NewOperator("Qyy", NF, IndexUp, IndexDn)
The operator could also be defined by:
Akm={{2,-2,-sqrt(1.5)},{2, 2,-sqrt(1.5)},{2,0,-1}}
OppQyy=NewOperator("CF",NF,indexup,indexdn,Akm)
charge_quadrupole indextext/html2025-11-20T02:29:35+00:00Anonymous (anonymous@undisclosed.example.com)Qyz
https://www.quanty.org/documentation/standard_operators/charge_quadrupole/qyz?rev=1763605775&do=diff
Qyz
The yz component of $Q$ is defined as:
\begin{equation}
Q_{yz} = 3yz/r^2.
\end{equation}
The equivalent operator in Quanty is created by:
OppQyz = NewOperator("Qyz", NF, IndexUp, IndexDn)
The operator could also be defined by:
Akm={{2,-1,sqrt(1.5)*I},{2, 1,sqrt(1.5)*I}}
OppQyz=NewOperator("CF",NF,indexup,indexdn,Akm)
charge_quadrupole indextext/html2025-11-20T02:29:35+00:00Anonymous (anonymous@undisclosed.example.com)Qzz
https://www.quanty.org/documentation/standard_operators/charge_quadrupole/qzz?rev=1763605775&do=diff
Qzz
The zz component of $Q$ is defined as:
\begin{equation}
Q_{zz} = 3z^2/r^2 - 1.
\end{equation}
The equivalent operator in Quanty is created by:
OppQzz = NewOperator("Qzz", NF, IndexUp, IndexDn)
The operator could also be defined by:
Akm={{2,0,2.0}}
OppQzz=NewOperator("CF",NF,indexup,indexdn,Akm)
charge_quadrupole indextext/html2025-11-20T02:29:36+00:00Anonymous (anonymous@undisclosed.example.com)Charge quadrupole operators (Q)
https://www.quanty.org/documentation/standard_operators/charge_quadrupole/start?rev=1763605776&do=diff
Charge quadrupole operators (Q)
The quadrupole operator is a special case of the crystal-field operator. The operator is defined as:
\begin{equation}
Q_{ij} = 3r_ir_j/r^2 - \hat{r}\cdot\hat{r}\delta_{i,j}.
\end{equation}
Whereby we need to note that we here only take the angular part of a quadrupole. It's “strength”, i.e. the expectation value of $r^2$charge_quadrupole index