Recent content by physiks

I seem to have two approaches that I've seen and understand, but I can't quite see how they relate. 1. Write a general time evolving state as a superposition of stationary states multiplied by their exp(-iEt/h) factors, and calculate <x>. We find that <x>=Acos(wt+b) as in classical physics (in...

Sorry, I know I said I was happy with everything, but I've tried to do this problem via another method, using the grand partition function and I seem to be misunderstanding something. I think for simplicity we can switch to the example of molecules in an isothermal atmosphere now - as on page...

Ah so it is all consistent, thanks a lot :)

Ok, I'm fairly happy with that. Going back to the first issue I was having, why is this the case: say we're considering the x component of kinetic energy... I believe P(E)∝exp(mvx2/2kT) here, and my book then says that P(vx)∝exp(mvx2/2kT), i.e that probability of having some vx2 directly...

Ok, so if the centrifugal force is F=mw2r then the potential is found by integration as -mw2r. However, I'm not entirely happy - why do I have to consider the centrifugal force (i.e the force observed in the rotating frame), and not the centripetal force (the force as observed outside of the...

Nope, I'm aware my E has the wrong sign - I'm not sure why though, surely KE is 0.5Iw2. The Boltzmann factor has the negative in...

Hmm I don't really understand it - say we're considering the x component of kinetic energy... I believe P(E)∝exp(mvx2/2kT) here, and my book then says that P(vx)∝exp(mvx2/2kT), i.e that probability of having some vx2 directly transforms into the probability of having vx. This seems to be fine so...

Do you mean I should have rn(r)∝P(E) instead of n(r)∝P(E) and so the factor r cancels meaning my P(E) is correct?

Homework Statement A cylinder contains an ideal gas and rotates at angular speed w. Find the probability that a molecule is at radial position r from the axis of the cylinder. Homework Equations Boltzmann distribution, P(E)∝Ω(E)exp(-E/kT) where Ω(E) describes the degeneracy of the energy level...

Thanks for your reply! So my notes say that it should give me a sinusoidal function, BUT, only over a finite interval - so we agree that they must be wrong then?

Changed a to d, didn't realize that. I'm not clear - the function b(x-y) is a box centred on y=x with width d, right? Then the integrand [1+sin(wy)]b(x-y) surely vanishes everywhere but for where the box is non-zero, and so basically we can write b(x-y)=1 as long as we integrate over the box...

Homework Statement According to my notes, if we have a sinusoidal aperture/transmission function of the form a(x)=1+sin(wx) and a 'top-hat' aperture function given by b(x)=1, -0.5d≤x≤0.5d, b(x)=0 otherwise, then their convolution should give a finite sinusoidal aperture function, i.e sinusoidal...

Oh I see, so my derivation basically assumes the whole system is in a steady state (transport properties are for steady state systems), because I used a fixed temperature gradient. So then the pressure and volume must be fixed (if the pressure was fixed but volume varied, my temperature would...

Ok, but I can't see why we started at constant V?

What does this mean?