Recent content by EricTheWizard

So consider a theory of a complex scalar field ##\phi## with a global U(1) symmetry ##\phi \rightarrow e^{i\theta} \phi##. The theory admits a conserved current $$ J^\mu = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)} \delta\phi + \frac{\partial \mathcal{L}}{\partial (\partial_\mu...

You're right; the problem does say to assume the system is thermodynamically large (N order of 10^23 or whatever). Sounds like a valid strategy (and makes the answer \nu(T)=\frac{g}{e^{\epsilon/kT}+g}). Thanks for the inspiration!

Hi everyone, I've hit a bit of a snag with part c of this problem (can't figure out how to invert a function T(ν)), so I'm starting to question whether I have the previous parts correct. Homework Statement Consider a system of N identical but distinguishable particles, each of which has a...

Is it valid to just take x as equivalent to the z direction (since the coordinates are arbitrary anyways) and define L_x Y_{lm} = m \hbar Y_{lm} and just solve it that way?

Could you explain this a bit more? I was under the impression that there were no L_x Y_{lm} eigenstates because the effect of the operator on the spherical harmonics is to raise and lower the "m" index, a la L_x Y_{lm} = \frac{1}{2}(L_+ +L_-)Y_{lm} =...

Homework Statement A particle is in the state \psi = R(r)(\sqrt{\frac{1}{3}}Y_{11} + i\sqrt{\frac{2}{3}}Y_{10})]. If a measurement of the x component of angular momentum is made, what are the possible outcomes and what are the probabilites of each?Homework Equations...

Ahh thank you for your post. So both vectors transform the same way, then. And just to make sure I have this right, you're saying that \frac{\partial}{\partial x_\mu} = \partial^\mu = \eta^{\mu\nu}\partial_\nu? So if I were to construct a relativistically-correct 4-momentum operator, would...

I'm slightly confused by the difference between covariant and contravariant 4-vectors and how they transform under Lorentz boosts. I'm aware that x_{\mu} = (-x^0 ,x^1, x^2, x^3) = (x_0 ,x_1, x_2, x_3), but when I do a Lorentz transform of the covariant vector, it seems to transform exactly like...

I always thought it was because the superposition of states was non-stationary, so if you had an ensemble of atoms with a given energy distribution, the possibility that anyone could be in any of a multitude of excited states is what causes the superposition, and hence non-stationary state

EM waves are deflected based on a variety of parameters, including wavelength, index of refraction, angle of incidence, and conductivity of a solid. General rules of thumb: the more conductive an object is, the more reflective it is. Also, EM waves tend to "ignore" the presence of objects...

Ahh I understand now, I had this picture in my head of some extraneous frame I guess I didn't need... Thanks for clarifying.

I've been learning about 4-velocity and all the "proper" 4-vectors recently, and if I understand correctly, proper velocity η (the 3-vector) is related to ordinary velocity by the relation \vec\eta = \frac{\vec u}{\sqrt{1-\frac{u^2}{c^2}}}, where u is ordinary velocity of an object within a...

ahh, it was adding and subtracting that E_i E_{i,i} that I was missing and was screwing me up. But I managed to work it out now. Thanks for your help!

Hi, I've been trying to derive the electromagnetic stress tensor on my own, and I've run into a bit of a problem. I have a cross product of a curl (\vec{E}\times(\nabla\times\vec{E})) that I need to expand, and the typical...