Changes

This is not an easy equation to solve without using a Fourier transform. Therefore, we'll do just that, with G as the transformed function.

This is not an easy equation to solve without using a Fourier transform. Therefore, we'll do just that, with G as the transformed function.

<math>G = \frac{1}{4\pi^2}\int{g(\Delta x,\Delta t)e^{-ik\Delta x}e^(i\omega\Delta t}d^3x dt}</math>

<math>G = \frac{1}{4\pi^2} \int{g(\Delta x,\Delta t)e^{-ik\Delta x}e^{i\omega \Delta t}d^3x dt}</math>

earlier equation. We can change

We will then need to plug this function into the earlier equation. To make this easier, we know that the four-dimensional delta function on the right-hand side can be simplified.

(copy equals-right-hand-side delta-function from

<math>\delta = \frac{1}{4\pi^2} \int{e^{-ik\Delta x}e^{i\omega \Delta t}d^3k d\omega}</math>

 

Now, we have an equation with integrals on both  

Now, we have an equation with integrals on both