Recent content by DragonBlight

So, can I replace the argument with u to find a "form" that I know for the delta function in every situation? For example, ##u = x^2 +2x -3## and ##x = -1 \pm \sqrt{u + 4}## Thus, I have ##e^{- 1 - \sqrt{u + 4}}## and ##\delta(u)## So we have ##\int_{-\infty}^{\infty} e^{-1-\sqrt{u+4}...

I'm not sure to fully understand. What should be the result? In a case where the argument is 0 only if x = 1, the result would have been ##e^{-1}##

Hi, Is it correct to say that the dirac delta function is equal to 0 except if the argument is 0? Thus, ##x^2 +2x -3## must be equal to 0. Then, we have x = 1 or -3. What does that means? ##\int_{-\infty}^{\infty} e^{-|x|}\delta(x^2 +2x -3) dx = e^{-1}## and/or ##e^{-3}## ? Thank you

##f(t) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi}} \frac{1}{(-\alpha -i\omega)^2} e^{i\omega t} d\omega## I don't see how to find the residue since the imaginary part is ##\omega##. There's a singularity ##\omega = i \alpha## I mean, if I had ##(-i\alpha - \omega)## I...

I made I mistake. It's ##te^{-at}##

Doing the Fourier transform for the function above I'm getting a result, but since I can't get the function f(t) with the inverse Fourier transform, I'm wondering where I made a mistake. ##F(w) = \frac{1}{\sqrt{2 \pi}} \int_{0}^{\infty} te^{-t(a + iw)} dt## By integrating by part, where G = -a...

I have another question. Can the modes be used as 5 different sources?

Section 2.3 of this document the author is talking about 2 frequencies but if instead of the 2 frequencies we have 5 different modes.

Homework Statement:: Find the interference function ##I(\delta)## where The emission is analyze by a Michelson interferometer. Relevant Equations:: ##I(\delta) = \frac{1}{2} \int_{-\infty}^{\infty} G(k) r^{ik \delta} dk## ##I(\vec{r}) = I_1 + I_i + 2 \sqrt(I_1 I_i) cos (k\delta)## I have 5...