Recent content by the_kid

I'm still having some trouble visualizing these processes...

I do have Mathematica!

Let M be the magnetic moment of a system. Below are the Bloch equations, including the relaxation terms. dM_x/dt=({\bf M} \times \gamma {\bf H_0})_x-M_x/T_2 dM_y/dt=({\bf M} \times \gamma {\bf H_0})_y-M_y/T_2 dM_z/dt=({\bf M} \times \gamma {\bf H_0})_z+(M_{\infty}-M_z)/T1 At t=0, {\bf...

Anyone?

Thanks so much for the help, micromass. The proof for the finite dimensional case relies on the fact that an eigenvalue of the operator can be found (at least the proof I'm familiar with). The operator Tf(x)=xf(x) on L^2[(0,1)] is obviously self-adjoint but has no eigenvalues. So, trying to...

So, obviously one can diagonalize any self-adjoint transformation on a finite dimensional vector space. This is pretty simple to prove. What I'm curious about is integral operators. How does this proof need to be adapted to handle integral operators? What goes wrong? What do we need to account...

That is perfectly normal. Typically professors will give hints on 3-star problems or students will discuss them with others and/or a teaching assistant. After obtaining some necessary "trick" through these discussions, the problems become much simpler, generally. Students that solve all of those...

I'm looking for a first-year graduate level stat mech textbook. What are the best ones out there?

OK, I've done some more reading on my own and now have a specific question. Hopefully this will get this thread moving. It is my understanding that for a quantum system to be locally gauge invariant, it must be in the presence of an EM field. I understand mathematically why this is true (at...

Hi all, I'm taking graduate level QM I and trying to wrap my head around the notion of gauge symmetry. For some reason I've struggled with this concept more than others. I don't really have a specific question; I'm more looking to see if someone has a succinct explanation of the relevant...

Well, I'm looking for math is relevant to high energy theory and/or condensed matter theory. If I knew what types of math were most relevant to those subfields, I wouldn't be asking the question. I don't really know how to narrow it down other than that. I've heard things such as K-theory...

No suggestions?

Hi all, I'm planning on doing a one-on-one tutorial my math department next semester. However, I don't know what topic I want to study, so I'm looking for some suggestions. Note that I'm interested in high energy physics (string theory, etc.) and theoretical condensed matter. I will be...

How exactly do I multiply these two together if they have infinite terms?

Homework Statement Consider the following integral: I=\int^{\pi/4}_{0}cos(xt^{2})tan^{2}(t)dt I'm trying to compute as many terms as possible of its asymptotic expansion as x\rightarrow\infty. Homework Equations x The Attempt at a Solution Let u=cos(xt^{2}). And...