List of useful equations

Here's a quick list of the most useful equations. If there's something that you find yourself looking up all the time, put it here!

In one dimension
$$F(k) = \frac{1}{\sqrt{2\pi}} \int f(x) e^{ikx} \, dx$$

In n dimensions
$$F(\mathbf{k}) = \left(\frac{1}{2\pi}\right)^{n/2} \int f(\mathbf{r}) e^{i\mathbf{k\cdot r}} \, d\mathbf{r}$$

Calculating resolution
Using the following definitions: