Recent content by erogard

Rotation is a bit of a misnomer indeed. I think unitary transformation is what is meant here. I'll try your first suggestion (just need to check it's indeed unitary) but it looks good to me. Thanks.

I think that works, since now T_22 = T_33 = T_44 so that T_{22}' = \cos^2(\theta')T_{22} + \sin^2(\theta')T_{33} = \cos^2(\theta')T_{22} + \sin^2(\theta')T_{22} = T_{22} and similarly for T'_33 and T'_44. Didn't check the off diagonal entries but they'd have to be zero. Also since the...

Thanks for the replies. ChrisVer: You are right regarding the last term, corrected that. If you look closely at (2.4), ignoring the addition term V[phi], this is really the same tensor up to an overall minus sign, I believe. George Jones: so, just to make sure: is the rotation matrix I'm...

Hi, I am trying to show explicitly the isotropy of the stress energy tensor for a scalar field Phi. By varying the corresponding action with respect to a metric g, I obtain: T_{\mu \nu} = \frac{1}{2} g_{\mu \nu} \left( \partial_\alpha \Phi g^{\alpha \beta} \partial_\beta \Phi + m^2 \Phi^2...

Hi, I am trying to derive the Lorentz force law in the following form: q \frac{dw^\mu}{d\tau} = q w^\mu \partial_\nu A_\sigma \epsilon_\mu^{\nu \sigma} by varying the following Lagrangian for a classical particle: S = \int d^3 x \left( -m \int d\tau \delta(x-w(\tau) ) + q \int d\tau...

Well, as you pointed out, for very small T we are pretty much dealing with a step function, so it should be identically 1 for energies below the fermi energy, and 0 above it since the higher states would now be unoccupied. So are you saying I should just use n_e = 1 when I integrate the DoS from...

A bit confused by this statement. Are you saying that what I wrote for obtaining the remaining number of particles, N', is inccorect? And why would the given expresssion for the new Fermi energy be any different? Aren't we still using N' = \int_0^{\epsilon_f'} D(\epsilon) d\epsilon and...

That would be N' = N - C \int_{\epsilon_f / 4}^{\epsilon_f /2} \frac{\epsilon^{1/2} d\epsilon}{\exp[(\epsilon -\epsilon_f)/kT] +1} correct? where C is a constant arising from the DoS. Don't know how to evaluate that integral though Then that's just \epsilon_f' = (\frac{3}{8 \pi})^{2/3}...

Originally thought of including the energy of the removed particles only, but yes I would assume that the transitional energies are to be included as well (kind of like when an electron drops to a lower orbit I guess)

So using the new N can I directly apply the definition E_f = (\frac{3}{8 \pi})^{2/3} \frac{h^2}{2m} (\frac{N}{V})^{2/3} ? assuming the particles rearrange themselves in the expectated way, i.e. the one left with energies higher than E_max will loose energy to refill those lower empty states...

Homework Statement Consider a 3D gas of N non-interacting fermions in a volume V at temperature T << Ef / k. Suppose that the particles in the energy range [0.25 Ef, 0.5 Ef] are suddenly removed. Calculate the Fermi energy of the remaining particles after the system reaches its new thermal...

Homework Statement Consider a system of 2 non interacting distinguishable particles in thermal equilibrium at temperature T, and which as two possible energy states available: E1 and E2>E1. How would you go about finding the average number of particles in energy level E1, and in height T limit...

So I did 1) by taking the log and exponentiating to simplify. Regarding 2), I'm looking at http://en.wikipedia.org/wiki/Central_limit_theorem and I'm assuming the Linderberg version is the relevant one here. Not too sure how to apply it, however. Do you know of any simpler formulation of the...

Homework Statement Suppose that particles of two different species, A and B, can be chosen with probability p_A and p_B, respectively. What would be the probability p(N_A;N) that N_A out of N particles are of type A? The Attempt at a Solution I figured this would correspond to a binomial...

anyone? just need a hint to get started really