更改

Note that we have used the fact that the phase space volume element <math> d^3\bf{r}</math>&nbsp;<math> d^3\bf{p}</math> is constant, which can be shown using [[Hamilton's equations]] (see the discussion under [[Liouville's theorem (Hamiltonian)|Liouville's theorem]]). However, since collisions do occur, the particle density in the phase-space volume <math> d^3\bf{r}</math>&nbsp;'<math> d^3\bf{p}</math> changes, so{{NumBlk|2=<math>\begin{align}

Note that we have used the fact that the phase space volume element <math> d^3\bf{r}</math>&nbsp;<math> d^3\bf{p}</math> is constant, which can be shown using [[Hamilton's equations]] (see the discussion under [[Liouville's theorem (Hamiltonian)|Liouville's theorem]]). However, since collisions do occur, the particle density in the phase-space volume <math> d^3\bf{r}</math>&nbsp;'<math> d^3\bf{p}</math> changes, so{{NumBlk|2=<math>\begin{align}

dN_{coll}&= \left ( \frac{\partial f}{\partial t} \right )_{coll}\Delta td^{3}\textbf{r}\, d^{3}\textbf{p}

dN_{coll} &= \left ( \frac{\partial f}{\partial t} \right )_{coll}\Delta td^{3}\textbf{r}\, d^{3}\textbf{p}\\[5pt]

&= f\left ( \textbf{r}+\frac{\textbf{p}}{m}\Delta t,\textbf{p}+\textbf{F}\Delta t,t+\Delta t \right )\, d^{3}\textbf{r}\, d^{3}\textbf{p}- f(\textbf{r},\textbf{p},t)\, d^{3}\textbf{r}\, d^{3}\textbf{p}

& = f\left ( \textbf{r}+\frac{\textbf{p}}{m}\Delta t,\textbf{p}+\textbf{F}\Delta t,t+\Delta t \right )\, d^{3}\textbf{r}\, d^{3}\textbf{p}- f(\textbf{r},\textbf{p},t)\, d^{3}\textbf{r}\, d^{3}\textbf{p}\\[5pt]

&=\Delta f d^{3}\textbf{r}\, d^{3}\textbf{p}

& =\Delta f d^{3}\textbf{r}\, d^{3}\textbf{p}

\end{align}</math>|3={{EquationRef|1}}|：}}

\end{align}</math>|3={{EquationRef|1}}|：}}