Recent content by curious george

A problem on my quantum homework assignment this week has to do with the projection operator P = |a><a| I've been asked to show that P^2=P, and then give the eigenvalues of P and then to characterize its eigenvectors. The first part is easy enough: P = |a><a| so P^2 = |a><a||a><a| =...

I'd appreciate it if I could get a little help on this one, I'm confused about how this is done. I know there are numerous papers out there about how to do this based on the SN1987A event that was detected with KII and IMB. The problem in my textbook asks me to make a rough estimate of the...

So the hamiltonian in this case is \left[\frac{1}{2m} \left(\frac{\hbar}{i}\bigtriangledown + qA\right)^2+q\phi\right] right? So if I take the commutator of that with x: \left[\left[\frac{1}{2m} \left(\frac{\hbar}{i}\bigtriangledown + qA\right)^2+q\phi\right],x\right] I should be able...

I'm sorry, this material is new to me and I'm not sure what is "standard" notation and what isn't. The question was asked in the context of gauge invariance in electrodynamics(that's what we're discussing in my class right now), so I believe the whole expression "p-qA" is the substitution...

I was recently given a problem that asked me to show that the classical velocity of a particle is given by: v = \frac{d \langle x\rangle}{dt} = \frac{1}{m} \langle({\bf p}-q{\bf A})\rangle The expectation value of the time derivative of x is given by: \langle v\rangle = \int{\Psi ^{*}...

An interesting side note is that, in natural units, where: \hbar = c = 1 The Planck mass is just the reciporical of the Planck length. L _{planck} = \frac{1}{M _{planck}}

Yes, that's exactly what you should do. 26.94 m/s is the velocity of a point on the outer rim of the wheel, so you can use that to calculate the angular frequency of the wheel.

I have a problem on my homework that lists several different reactions involving K mesons and asks which of them can happen via the strong interaction. I've listed a couple of them below, and I'm hoping that someone can tell me why these can or can't proceed via the strong interaction: (K-)...

First, consider the smallest energy x length that you can have, which is dictated by our knowledge of quantum mechancs: \hbar c Now set that equal to the gravitational energy to get it in terms of the gravitational constant: equation 1 GM^2=\hbar c solve for M and you get the Planck...

I don't understand why the pi(+) has such a long lifetime compared to the pi(0). Can anyone give me a simple qualitatiive explanation of this?