Recent content by 2Tesla

That's a very good explanation of a different question :) What I meant to ask was: why do red lifeguards swim faster than blue lifeguards (i.e. why does lower-frequency light have a lower index of refraction than higher-frequency light, in, say, water at visible wavelengths)?

Sounds like a mistake to me--the quickest way to see this is to note that n is unitless while k has units of inverse length. If you're treating n as the complex index of refraction, and k as the complex wavevector, then the formula k = n*omega/c still holds.

I'm thinking of normal dispersion, of course, far from any resonances, say in bk5 glass or water. I thought it might be due to higher-frequency light undergoing more collisions, but I'm not sure. Thanks!

The center of mass is at the center of the cylinder regardless of whether it is full or hollow. This is obvious by the rotational symmetry of the cylinder.

This is incorrect. If the cylinder rolls without slipping, then w=v/r. If it is full, then moment of inertia I=(1/2)mr^2 and we have rotational energy = (1/2)*translational kinetic energy: R=(1/2)Iw^2 = (1/2)*((1/2)mr^2)*(v/r)^2 = (1/4)mv^2 = K/2 If, however, the cylinder...

But clearly that's not possible. For example, let A=p_{x}, B=x, C=y Then [A,BC] = [p_{x},x]*y = -i \hbar *y and [A,B] = -i\hbar, [A,C] = [B,C] = 0 There just isn't any way to do it. I think they mean to write it as an expression where the commutators involve only two...

Your answer will involve a sum of the products of the original operators with the two-operator commutators, as in: X*[Y,Z] or [X,Y]*Z Where X, Y, and Z are each one of A, B, and C. (I wrote it this way to avoid giving the answer away :)

First, let's say you had a uniformly charged insulator that was arbitrarily large in all 3 directions. Would there be any potential in it? Why (not)? Now think about what happens if it's only arbitrarily large in y and z, but in x has some finite width. As for the exercise, you don't need...

You may find this useful: http://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html"

Don't forget about n1=3, n2=n3=1, and its permutations. Do you understand why the 3rd level is degenerate? That will be necessary to determine which of the 4th, 5th and 6th levels might be degenerate also.

Why do you think that? It's not given anywhere in the problem statement that each atom can only have one electron. Remember that the Pauli exclusion principle only rules out two indist. particles in the *exact* same state...

Let's be a little more concrete, here. Say we're considering a single particle with momentum eigenvalues p1, p2, ... Now, Carroll is talking about wavefunction collapse after a measurement, which means that the particle is interacting with another system. So, when he says that a...

I'm all for waiting as long as possible to specialize, but as a soon-to-be 1st year grad student... it's getting to be time. Not that you can't study other subjects, but how hard you need to work on math right now and your 1st-year courses really do depend on what field you'll work in. I'll...

If you're planning on taking even just GR and field theory your first semester, you will be very glad to have some diff geom, complex analysis, group theory, etc. under your belt, before starting. If you decide not to take the extra semester, studying them over the summer would not be a bad idea.

Who is? I'm referring to the third question of: http://www.sciam.com/article.cfm?id=times-arrow-faqs" which is a supplement to the Carroll article: http://www.sciam.com/article.cfm?id=the-cosmic-origins-of-times-arrow" But regardless of where it came from, can anybody help me...