Recent content by Backpacker

A paper I'm reading states the that: for positive hermitian matrices A and B, the Taylor expansion of \log(A+tB) at t=0 is \log(A+tB)=\log(A) + t\int_0^\infty \frac{1}{B+zI}A \frac{1}{B+zI} dz + \mathcal{O}(t^2). However, there is no source or proof given, and I cannot seem to find a...

Hold on, I guess I see where some of my confusion is coming from. In class, we showed that under a Lorentz transformation ##\Lambda##, the current (just like any good 4-vector) transforms as ##j'^\mu={\Lambda^\mu}_\nu j^\nu##. But I guess this is only for proper orthchronous transformations...

Ok, so I'm comfortable with the fact that the spatial components of the current are inverted under time reversal, i.e. ##{j'}^i=-j^i##. But, why is ##j^\mu A_\mu## invariant? And what does ##j^\mu A_\mu## mean physically?

Consider the time-reversal Lorentz transformation given by the 4x4 matrix: \Lambda_T = \begin{pmatrix} -1 & 0 & 0 & 0\\ 0 &1 & 0 & 0\\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 &1 \end{pmatrix}. In my relativistic quantum mechanics lecture, we discussed how the electromagnetic 4-potential...

I am in the middle of doing something very similar! I studied physics, and had a German minor and went for an exchange semester during my junior year and really enjoyed it. Then, in my last year of my undergraduate studies in the United States, I fell terribly ill. I missed a few weeks of...

Hey, So I've talked to my advosor, and he more clearly described the problem that he thinks we will have. Look at the attached picture. He wants to measure the blue line, but fears that if we simply measure the DC signal that it will give us the red line. I told him that I don't...

Ok, so I am just an undergraduate intern this summer. We have light source shining through an optical chopper, reflecting of a lit display, and going to a detector. So, we have a signal on top of a DC signal coming from the fact that the display is also emitting light. We want to measure...

PS. This field is entirely new to me, and my adviser is not very helpful on this. (In fact, most of what he gives me to do is cleaning/splicing fiber optics and soldering. Very boring. I am more or less doing this digital filtering stuff on my own because he often mentions that it is the...

So I'm a physics major who is doing a summer research internship that is mostly electrical engineering. My research adviser is also a physicist and doesn't really know much about this either. But essentially what we need is take an analog signal and digitize it (to about 100 MHz), and use a...