Recent content by kairosx

I'm not sure if I understand what you mean. Actually, I really don't like the square and arctan expressions either, but how else would you do it? You mean expressing ##x_1## and ##x_2## in terms of ##r## and ##\theta## like ## x_1 = r cos \theta ## and ## x_2 = r sin \theta ##? But if I then...

Okay, thanks for the tipps about the notation and sorry again for the confusion about the vector identity! :-) I tried to come forward now by considering ## r = \sqrt{x_1^2 + x_2^2} ## ## \theta = arctan(\frac{x_2}{x_1}) ## ## \frac{dr}{dx_1} = \frac{ x_1}{\sqrt{x_1^2 + x_2^2}} = \frac{...

But ## x \in R^2 ## is a vector ## x = (x_1,x_2)^T ## and how is ## \frac{1}{vector} ## is defined? Okay, i started once again: ##x \in R^2## is a vector with the components ##x = (x_1,x_2)^T## $$ \frac{ \partial (x_1/|x|^2) }{\partial x_1} + \frac{ \partial (x_2/|x|^2)}{ \partial x_2} =\\ -...

Actually by saying that ## x \in R^2 ## i always mean ## \int dx := \int d(x_1,x_2) ##, i definitely should have stated that explicitely. Okay, i going to start from scratch with the distributional derivative for my vector field :-) $$ <\frac{d}{dx_1} \frac{x}{|x|^2} + \frac{d}{dx_2}...

You mean like $$\frac{d}{dx_1} (\frac{1}{|x|^2}) = < \frac{d}{dx_1} \frac{1}{|x|^2},\phi(x)> = - <\frac{1}{|x|^2}, \frac{d}{dx_1} \phi(x)> = -\int_{-\infty}^{\infty} \frac{1}{|x|^2} \frac{d}{dx_1} \phi(x) dx = - \int_{0}^{\infty} \frac{1}{x^2} \frac{d}{dx_1} \phi(x) dx - \int_{-\infty}^{0}...

Homework Statement Show that $$div ( \frac{x}{|x|^2} ) = 2 \pi \delta_{(0,0)}$$ with ## x \in R^2 \ \{ 0 \} ## and ## \delta_{(0,0)} ## beeing the dirac delta distribution with pole in ## (0,0) ##. Homework Equations ## div (f(x)) = \nabla \cdot (f(x)) = f_{x_1} + f_{x_2} ## The distribution...

Hey, I'm watching it too. I also think it's really great produced. Which special part from last nights episode are you talking about? I haven't even watched X-Men, so i had to google the background story to find out about the original "Legion" Character in the X-Men universe...

Hi! I recently learned about the Alpha decay, where the atomic Nukleus emittes Alpha-Particles. I was wonderin if a material, which emittes such Alpha Particles has a surplus of electrons and so a negativ electronic charge after the decay. Because it loses Protons but stays with the...

Hi! We were recently discussing if time appears quantified. I found the theory about "chronons" (quantums of time) on Wikipedia and I know, those are very theoretical constructs and as far as I found out there is no current research if chronons even exist. But I was wondering if somebody has an...

Awsome! Thank you, i like this Board ;)

I have a question: Is there an Android App, through which I can use physicsforum?

Hello, I study technical physics at the technical university in Vienna. I'll start my third semester in october and I'm looking forward to interesting discussions in this online forum! :-) cu, kariosx