Recent content by stephen cripps

Ah thanks! I've got there now. On the solution sheet they seem to suggest a different method using f''(r) but don't show it explicitly but this definitely seems valid. (Though I think the + should be a - in your third equation after splitting the fraction.)

Homework Statement The final part of the problem I am trying to solve requires the proof of the following equation: \frac{d}{dr}(\frac{rf'(r)-f(r)+f^2(r)}{r^2 f^2(r)})=0[/B]Homework Equations I've been given the ansatz: f(r)=(1-kr^2)^{-1} leading to f'(r)=2krf^2(r)...

So starting from 6.24, by bringing the b inside the square root, I can replace (1-b^2V(r))^{1/2} With (1-\frac{r_1^2}{r^2}(1-\frac{2M}{r}+\frac{2M}{r_1}))^{1/2}. Ignoring higher orders of M. Expanding this again however doesn't seem to get me near the right answer.

Hi, thanks for you reply Sorry I made a mistake in my first statement, where I put my integral in section 3 tit should show t=\int_{r_1}^r(1+\frac{2M}{r}+\frac{b^2}{2}[\frac{1}{r^2}-\frac{4M^2}{r^4}])dr Referring back to your solution though, is the argument not already in first order of M...

Homework Statement The step I am trying to follow is detailed here where I am trying to get from equation 6.26: t=\int_{r_1}^{r}(1+\frac{2M}{r}+\frac{b^2V(r)}{2}+\frac{Mb^2V(r)}{r})dr to equation 6.30 t=\sqrt{r^2-r_1^2}+2Mln(\frac{r+\sqrt{r^2-r_1^2}}{r_1})+M(\frac{r-r_1}{r+r_1})^{1/2} Homework...

Oh yeah, I have it now. I was being stupid.

This is the part of the problem I'm having trouble with

Homework Statement We have the equation ## (\frac{dr}{ds})^2+(\frac{l}{r})^2=1 ## and want to solve to get ## r=\sqrt{l^2+(s-s_0)^2}## Homework EquationsThe Attempt at a Solution I have worked backwards, plugging in the solution to prove that it is correct, but the closest I have gotten to...

Awesome this was exactly what I needed. THANKS!

Homework Statement In order to use cauchy's residue theorem for a question, I need to put ##f(x)=\frac{z^{1/2}}{1+\sqrt{2}z+z^2}## Into the form ##f(x)=\frac{\phi(z)}{(z-z_0)^m}##. Where I can have multiple forms of ##{(z-z_0)^m}## on the denominator, e.g...

Yeah I think I understand that now, thanks a lot for your help, I see I need to be a lot more careful with what is just a component and what is a matrix. Hopefuly that will come with more practice of this notation.

Ok I see how that works now I think. As there's no implicit sum its just the component of a vector. Am I right in thinking though that a subscript usually indicates a row vector, and a superscript a column?

I assumed them from the vector representation section

Homework Statement I'm having trouble with understanding four vectors in particle physics. I'm reading this wikipedia page,http://en.wikipedia.org/wiki/Einstein_notation, and its telling me that ## v^\mu= \begin{pmatrix} \mu_0 \\ \mu_1 \\ \mu_2 \\ \mu_3 \end{pmatrix} ## and ## v_\mu=...

Homework Statement (This isn't coursework, just a revision question) Exercise: An ellipse can be defined as the locus of all points, P, in the plane such that PF_1+PF_2=\frac{2p}{(1-ε^2)} where F1 and F2 are two fixed points, and PF1 is the distance from P to F1 (similarly, P F2). F1 and F2 are...