Recent content by chris_avfc

Homework Statement Our lecturer seemed to skip over how to get from the Group Velocity Dispersion to the actual temporal stretch of a pulse sent down an optical fibre, instead we were given just the two formula. I've been trying to work out where the temporal stretch comes from but can't work...

Okay well I can't seem to find a way to edit the original post so I'm going to reply with what I've got so far. I've been looking at the trigonomic hyperbolic identities and their differentials. If we have ## x = a tanh^2(\eta) ## then ## dx = 2tanh(\eta)sech^2(\eta)d\eta## ## y = a\theta ##...

Homework Statement I've been given the line element given below in the relevant equations section and I need to prove that the space it represents is just the same as the 2-D Euclidean plane. Homework Equations ds^2 = a^2 \frac{d\eta ^2 }{cosh^4(\eta)} + a^2 tanh^2(\eta) d\theta ^2 Where...

Ah of course, so I calculated the eigenvalues of ##S_z## were ## 1, 0, -1 ## all multiplied by ##\hbar##, therefore the possible results of a measurement would be ## \hbar, 0, -\hbar ##. But then I'm unsure how you calculate the probability because I don't get what you substitute in for ##...

Are these values affected by the initial state of the system though?

Haha, thanks for that was having a little trouble with that code. Hmm, I think I might have been really stupid here. Previously I calculated the eigenvalues and eigenvectors for the three spin operators ##S_x , S_y , S_z##, which I presumed was unrelated, but thinking about it they probably...

$$\frac{\hbar}{\sqrt2} \left(\begin{array}{cc} 0&1&0\\1&0&1\\0&1&0\end{array}\right) $$ Mod note: fixed your LaTeX for you.[/color]

Is the relationship needed for to get the ##S_x##, the formula to get the ##S_x## eigenstates in the terms of the ##S_z## basis? I thought it would have to do with the relationship given, but I'm struggling to find anything. Also am I wrong in thinking ##m = +1,-1, 0##?

Is ## m ## just an constant then? Does that mean the actual measured value is just ##m\hbar## then, where the m changed depending on which spin state it is?

Going through my lecture notes from the start of the year looking for the relevant stuff. I think this is where I might be getting my idea of the operator acting from "3. In classical mechanics it is always assumed that the value of an observable may be measured without acting the state of...

Well I thought that the operator would act on the system, meaning I would apply ##S_z## to ##\psi##, but now I'm thinking that is wrong.

Oh right, that makes a lot more sense thinking about it, considering you have the momentum operator and position operator. Have I got this completely wrong then, but I thought when you make a measurement you change the wavefunction, as in would is not change from ##\psi## to ##\phi##? Awesome...

I thought that at first, but googling it I saw that there was a bit about Dirac saying they are possible, so I though it may be possible. To start, you need to familiarize yourself with two basic concepts in QM: Am I right in thinking that if you take a measurement or an observable the...

I can't see anything about which axis it is projected on, I thought at first that maybe each term represents projection on a different axis. I need to find results of the measurement for ##S_z## and ##S_x## though. If they are projected along the ##S_z## axis, I'm guessing the expression for...

Homework Statement Spin-1 Particles prepared in the state: $$ |\psi> = \frac{2}{\sqrt29} |1> + \frac{i 3}{\sqrt29}|0> - \frac{4}{\sqrt29} |-1> $$ Where I'm guessing the ## |#> ## represents the spin state of -1,0 or 1. I'm looking to find the results of a measurements of the ## S_x ##...