Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have a vector function (momentum [tex]\vec{p}(x,y,z)=\vec{p}(\vec{r},z)[/tex] for [tex]\vec{r}=(x,y)[/tex]) and need to transform it, also I use the fourier transform

[tex]F(\vec{p})=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \vec{p}(\vec{r},z) exp^{i \vec{\chi}\cdot \vec{r}}d\vec{r}[/tex]

and then

when I have in the equation laplace operator,

[tex]\Delta\vec{p}(x,y,z)=\Delta\vec{p}(\vec{r},z)[/tex]

which I have transformed, what is the appropriate expression for it?

[tex]\Delta\vec{p}(\vec{r},z)\rightarrow (FT)\rightarrow ???[/tex]

is it this?

[tex]\Delta\vec{p}(\vec{r},z)\rightarrow (FT) \rightarrow (\chi^2+\frac{\partial^2}{\partial z^2})\vec{\hat{p}}(\vec{\chi},z)[/tex]

is this right?

thank you for your help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 2D Fourier of 3D (vector) function - laplace of it?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**