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--- forcebalance:equation_of_motion [2023/11/22 11:08] – Field operator cjoens
+++ forcebalance:equation_of_motion [2023/11/22 12:42] (current) – [Current Density Operator] cjoens
@@ Line 32: / Line 32: @@
   \nu (\vec{r}^\prime,\vec{r})
 \end{equation}
+=====Particle Number Operator=====
+The EoM of the particle number operator
+\begin{equation}
+  \frac{\partial}{\partial t} \hat{n}_\text{H}=
+  \dots
+\end{equation}
+is of the form of a [[forcebalance:continuity equation]].
+The calculation is done [[forcebalance:calculation:EoM particle number operator|here]].
 =====Current Density Operator=====
 Wtih the help of the EoM of the fermionic field operator, the EoM for the current density operator $J(x,t)$ becomes
 \begin{equation}
-  \frac{\partial}{\partial t} J (x,t)
+  \frac{\partial}{\partial t} \hat{J}_\text{H} (x,t)
   =
+  \frac{\partial}{\partial t} \hat{j}_\text{H} (x,t)
+  +
+  \frac{\partial}{\partial t} \hat{j}_\text{d,H} (x,t)
+  =
+  \dots
+  +
   \dots
   \quad .
 \end{equation}
+FIXME Insert Link to para and diramagnetic definitions
 This holds for symmetric correlation potentials
 \begin{equation}