Hello.
I have this function ## v(x) = -\sum_{i=1} x^i \sqrt{2}^{i-2} \int_{-\infty}^{\infty} m^{i-1} \cosh(m)^{-4} dm## which I can not seem to figure out how to simplify.I tried looking at some partial integration but repeated integration of ## \cosh ## gives polylogarithms which seemed to...
(Sorry for the terrible title. If anybody have a better idea, post and I will edit. Also I have no idea of the level so now I just put undergraduate since the problem is fairly easy to state.)
Suppose I buy ## N## sensors which the manufacturer tells me will fail at some point and the failure...
Hi all.
Sometimes I have a few questions in my head I like to post at some point but which at the moment aren't completely ready. It would be nice if we had some personal draft section where I could write down my question and do updates and so on before releasing it for the general public...
Hallo.
So the other day I reviewed a bit of quantum field theory and went through the Compton scattering calculation. To no ones surprise it was fairly simpel if you have a nice list of identities for rewriting the base results from the Feynman diagrams. See for exaxmple section 5.3 in...
Hi everyone! After a few slow days in the office I thought I would like to derive the 2-point correlation function within statistical(Euclidian) ## \phi^{4} ##-theory but I ran into some problems. For the sake of clarity I will show you from where I startet and ask questions when I need help...
With
$$
H = \alpha \left(x^{2}\partial_{x} - x \partial_{x} \right) + \beta\left(x \partial_{x}^{2} - x^{2}\partial_{x}^{2}\right)
$$
Sorry for the messed up tex. I don't know how to fix it. It works in my editor.
Hallo PF! This might become a somewhat long post so for the...
Hi. First off, sorry for the not so descriptive title. If one of you finds a better tilte I will edit it.
We have the equation
\begin{equation}
\partial_{xx}\phi = -\phi + \phi^{3} + \epsilon \left(1- \phi^{2}\right)
\end{equation}
We will look for solutions satisfying...
Hi everybody! First post!(atleast in years and years).
The stationary KdV equation given by
$$ 6u(x)u_{x} - u_{xxx} = 0 $$.
It has a solution given by
$$ \bar{u}(x)=-2\sech^{2}(x) + \frac{2}{3} $$
This solution obeys the indentity
$$ \int_{0}^{z}\left(\bar{u}(y) -...