Recent content by thegreenlaser

That example doesn't satisfy the required condition (#poles)>(#zeros)+1. The key to the whole thing is that the integrand needs to go to zero faster than ##1/z##. Interestingly, though, the inside-outside theorem still seems to apply to your example if you include poles at infinity. The residue...

Yes, I can assume ##X(z)## is meromorphic. I'm a little confused by your analysis... unless I'm misunderstanding, it seems to neither prove nor disprove my assertion. Yes, the integral will be equal to the residues inside ##C##, but I'm effectively arguing that those residues must add up to...

This relates to z-transform causality, but I'll try to phrase it as a complex analysis question. Suppose I have a function ##X(z)## whose poles are all inside the unit circle, and which has the property \lim_{|z|\to\infty} \frac{X(z)}{z} = 0 Is that sufficient to guarantee that \frac{1}{2\pi...

I keep hearing about things like "quantum decoherence" and the notion that measurement doesn't need a conscious observer. However, I haven't really seen these topics discussed in any of the textbooks I've used (mostly on the level of Griffiths and higher). I haven't even seen a reference to...

You kind of get to pick and choose how rigorous you want to be. Obviously there are a slew of "modern physics" books that teach simplified quantum theory using algebra and calculus. To learn it "properly," though, you probably want to learn it in terms of abstract Hilbert spaces and linear...

I would actually disagree. Most of what students learn in high school is not really useful in most workplaces. Most people get by just fine without ever needing to solve quadratic equations or look for symbolism in classic literature. I feel like high school is more oriented towards giving...

I'm obviously not an expert in literature reviews, but have you tried Google Scholar? It's way better than regular Google for this kind of thing, since that's what it's designed for. It's certainly not the only search engine you'll ever need, but it's not a bad place to start.

For context, I'm working as an undergraduate researcher for the summer. Last week I felt like I was on a roll. Everything was going my way and I ended up deriving an interesting method which was different from anything anyone in my research group had heard of. With my method hashed out, it was a...

In Lagrangian/Hamiltonian mechanics, what is it that makes phase space special compared to configuration space? As a simple example, if I use ## q ## as my generalized position and ## v = \dot{q} ## as my generalized momentum, then the Hamiltonian H = \frac{1}{2} v^2 + \frac{1}{m} V(q) gives...

It depends, I think. The core material of an introductory differential equations course is not that hard to learn on your own. It's basically just a matter of learning a bunch of different types of equations and remembering the "trick" for solving each type. In my experience, the challenge was...

Yep! As I understand, nanorobotics is something you would usually specialize in after doing a more general degree like physics or engineering. If possible, find a university which does research in nanorobotics, but it's not the end of the world if you don't. Like I said, I'm doing my undergrad...

Why not study something like electrical engineering, maybe with a minor or double-major with physics? As far as I know, most people who end up in Nanotechnology don't actually have a degree in "Nanotechnology." They'll have a degree in electrical engineering, mechanical engineering, physics, or...

The further you get into physics, the harder it will be to find good animations. There are a number of reasons I see for this. 1) As mfb mentioned, it's really hard to come up with a good way to visualize complicated systems. Electromagnetic fields are tough to visualize, because you're trying...

I'm finishing up an electrical engineering degree with a minor in physics and I'm applying to grad school right now. The physics minor actually seems to carry a decent amount of weight in a grad school application. I had a few potential advisors tell me that my physics minor was what really...

I'm guessing you're thinking of the simplest case, where gravity is the only relevant force. In that case, it can't be done. The gravitational force is independent of the speed; you'll always measure a downward force of about (9.8 m/s^2)*(mass of ball), regardless of the speed. So the...