- #1
Dopplershift
- 59
- 9
Homework Statement
\begin{equation}
\int_V (r^2 - \vec{2r} \cdot \vec{r}') \ \delta^3(\vec{r} - \vec{r}') d\tau
\end{equation}
where:
\begin{equation}
\vec{r}' = 3\hat{x} + 2\hat{y} + \hat{z}
\end{equation}
Where d $\tau$ is the volume element, and V is a solid sphere with radius 4, centered at the origin.
Homework Equations
The Attempt at a Solution
I know the following:
Suppose:
\begin{equation}
\int_V f(r) \delta^3(\vec{r}-\vec{r}') d\tau = f(\vec{r'})
\end{equation}
(if r' is in the volume).
I'm just confused on how to plug in r' into f(r) which is
\begin{equation}
r^2 - 2\vec{r} \cdot \vec{r}'
\end{equation}
Any help to get me started will be much appreciated.