Recent content by Paul Colby

Isn’t it reasonable to say mathematics, in it’s beginning, began by fitting nature? People built logical systems around things about the world they observed?

Ah, it’s Mellin transform, which I haven’t heard of either. But a quick read of the Wiki page suggests contour integration to me. Where are the poles of ##\Gamma(s)^2## in the complex ##s##-plane?

My masters thesis involved Mei scattering. We were interested in quantifying the effects of multiple scattering on measurements of binary phase transitions in fluid mixtures. People used laser light to measure these systems which could become quite turbid. Anyway, cloud particles range from 5 to...

It’s your turn to feed the alien.

Rutherford measured the differential cross section. Its main feature, what most alphas did, is described by coulomb scattering, which had (has) a well understood model prediction. The coulomb cross section is strongly peaked at small scattering angles and falls off for higher angles. The smaller...

If you’ve an advanced degree from a university, perhaps contacting them? Also, journals have review processes. Some may even waive publication costs. However, if the paper is not of interest to an active community, you’re likely out of luck. One quick check of this will be the papers you’ve...

Even for a single particle, the Schrodinger equation describes many different possible situations. The hydrogen atom has a unique ground state, however, the Schrodinger equation allows for a ground state hydrogen atoms in any state with any velocity. Typically one is interested in atoms at rest...

Doesn't this have to do with time translation invariance of the medium? This, of course, may be traced back to energy conservation. Triangular waves aren't multiplied by a constant when the time derivative is taken.

Ah, yes. It's not even implicit. I'm still mystified by this discussion, so I'll just not comment further.

So, I look at this and the set ##x^2<0## isn't empty. ##2i## is a member for example.

With more than two particles things become more complicated. The space and spin wave functions can have mixed symmetry, neither symmetric nor asymmetric. The net function must be symmetric, though.

The states are defined in terms of the tensor product of the single particle states, $$\mathbf{l}_1\otimes\mathbf{l}_2$$ This space has ##(2l_1+1)(2l_2+1)## vectors. Selecting combinations that are eigenvectors of ##L^2## and ##L_z## is done with the Clebsch-Gordan coefficients. The symmetry...

I don't use GNU Radio but I've done some IIRs using liquid-dsp. My suggestion is to look at the source code for the IIR block. Walk through what it's actually calculating for the inputs you've given it. The one nice thing about open source is you have the source.