Recent content by bananabandana

Given a two particle scattering problem with (initial) relative velocity $|\vec{v}|$, apparently the product $E_{1}$E_{2}|\mathb{v}|$ can be expressed in the covariant form: $$ E_{1}E_{2}|\vec{v}| = \sqrt{ (p_{1}\cdot p_{2} - m_{1}^{2}m_{2}^{2}} $$ My textbook gives no further explanation -...

If we have the normal KG scalar field expansion: $$ \hat{\phi}(x^{\mu}) = \int \frac{d^{3}p}{(2\pi)^{3}\omega(\mathbf{p})} \big( \hat{a}(p)e^{-ip_{\mu}x^{\mu}}+\hat{a}^{\dagger}(p)e^{ip_{\mu}x^{\mu}} \big) $$ With ## \omega(\mathbf{p}) = \sqrt{|\mathbf{p}^{2}|+m^{2}}## Then why do we associate...

For reference, I'm at ICL :P

Sure - well, if anything I think King's might have a shade on Edinburgh course wise as 'Wastrophysicist' points out - it's been going for longer, and they (guess it's obvious since they have John Ellis) have more stuff on supersymmetry and strings. But then supposedly Imperial is better than all...

Hey - haha well... as a physicist, it's my duty to warn you that's a bad basis on which to make a decision :) Otherwise, I'm going to be heading up north to Edinburgh!

Homework Statement Why does Thomson scattering occur in the early universe? Homework Equations $$ e^{-} + \gamma \rightarrow e^{-} + \gamma $$ is a Thomson scattering process if: $$ E_{\gamma} << m_{e}c^{2}$$ (Electrons are essenitally stationary) The Attempt at a Solution [/B] Very confused...

Problem solved! The point is that at matter radiation equality, we must have that: $$ \frac{\rho_{M}}{\rho_{R}} = 1 $$ This does NOT mean that: $$ \frac{\Omega_{M}}{\Omega_{R}} = 1 $$ Since : $$ \frac{\rho_{M}}{\rho_{R}} = \frac{\frac{\Omega_{M}}{a^{3}}}{\frac{\Omega_{R}}{a^{4}}} =...

Homework Statement Show that the time of matter-radiation equality, t_{eq} can be written: $$ t_{eq} =\frac{a_{eq}^{\frac{3}{2}}}{H_{0}\sqrt{\Omega_{m}}} \int_{0}^{1} \frac{x}{\sqrt{x+1}} dx $$ Homework Equations $$ t = \int_{0}^{t} dt = \int_{0}^{a} \frac{1}{H(a)} \frac{da}{a} $$ [Given]...

Hi all, I have an offer to do an MSc in QFFF at Imperial or an MSc in Mathematical Physics at Edinburgh, or (with luck) an MSc in Theoretical Physics at Kings College London (KCL). Technically, QFFF is the best (i.e most reputable) course - but I have heard very bad things about how it's...

Homework Statement Let ## \mathbf{r} ## be the position of a point in a rigid body relative to some origin ##O##. Let ##\mathbf{R}## be the position of the centre of mass from that origin. ##\mathbf{r^{*}} = (\mathbf{r}-\mathbf{R})##. ## d\boldsymbol{\phi} ## is the infitesimal vector directed...

Seems about right! :) I don't know what you're wanting to do (are you an engineer, is this a hobby, etc.?) but another good resource is the Feynman lectures Vol II - http://www.feynmanlectures.caltech.edu/II_01.html You can't really dip in and out of them - it's probably best to make time to...

Ah, of course. No, it's definitely not rotating about S. Thank you. Also realize now that the definition of the intertia tensor only involves motion about the centre of mass, so obviously it doesn't take the angular momentum relative to the origin at $S$ into account. So then I get this- that...

Why aren't the two the same? Surely the whole system is connected and therefore has the same ##\omega##

Ah no, sorry - it should be ##L## . This was part of a final year exam question, so I'm pretty sure I must be wrong somewhere!

Homework Statement A door ( a rod of length ##L##, mass ##M##) rotates with angular velocity ##\omega## about a point ## H ##, and approaches a stop at ##S##. ##H## and ##S## are along the same line, and separated by a distance ## s ##. Show that the angular momentum of the door about the point...