- #1
LocationX
- 147
- 0
For some reason I can't post everything at once... gives me a "Database error" so I will post in parts...
A vector function can be decomposed to form a curl free and divergence
free parts:
[tex]\vec{f}(\vec{r})=\vec{f_{\parallel}}(\vec{r'})+\vec{f_{\perp}}(\vec{r'})[/tex]
where
[tex]\vec{f_{\parallel}}(\vec{r'}) = - \vec{\nabla} \left( \frac{1}{4 \pi} \int d^3 r' \frac{\vec{\nabla'} \cdot \vec{f}(\vec{r'})}{|\vec{r}-\vec{r'}|} \right)[/tex]
and
[tex]\vec{f_{\perp}}(\vec{r'}) = \vec{\nabla} \times \left( \frac{1}{4 \pi} \int d^3 r' \frac{\vec{\nabla'} \times \vec{f}(\vev{r'})}{|\vec{r}-\vec{r'}|}[/tex]
I am trying to take the Fourier transform of [itex]\vec{f_{\parallel}}(\vec{r'})[/itex] and [itex]\vec{f_{\perp}}(\vec{r})[/itex]
A vector function can be decomposed to form a curl free and divergence
free parts:
[tex]\vec{f}(\vec{r})=\vec{f_{\parallel}}(\vec{r'})+\vec{f_{\perp}}(\vec{r'})[/tex]
where
[tex]\vec{f_{\parallel}}(\vec{r'}) = - \vec{\nabla} \left( \frac{1}{4 \pi} \int d^3 r' \frac{\vec{\nabla'} \cdot \vec{f}(\vec{r'})}{|\vec{r}-\vec{r'}|} \right)[/tex]
and
[tex]\vec{f_{\perp}}(\vec{r'}) = \vec{\nabla} \times \left( \frac{1}{4 \pi} \int d^3 r' \frac{\vec{\nabla'} \times \vec{f}(\vev{r'})}{|\vec{r}-\vec{r'}|}[/tex]
I am trying to take the Fourier transform of [itex]\vec{f_{\parallel}}(\vec{r'})[/itex] and [itex]\vec{f_{\perp}}(\vec{r})[/itex]