Recent content by RGann

I think this is the answer. Strangely, the text seems to confuse the scattering amplitude with the form factor. As Charles says, the extra ##1/q^2## is factored out of the form factor. This is also present in F. Scheck, Electroweak and Strong Interactions, eqns 2.5-2.6. Only Krane seems to skip...

Sorry to resurrect this thread, but I'm not getting it. Like y'all, I have $$ e^{i\mathbf q \cdot \mathbf r'} \int e^{iqu \cos \theta} u \sin \theta du\,d\theta\,d\phi $$ When iterated (and doing the ##\phi## part) $$ 2 \pi e^{i\mathbf q \cdot \mathbf r'} \int_0^\infty u \int_{-1}^1 e^{iqu...

I've pored over a few treatments of the problem in available texts at the library. Abdul Jerri has a book on the Gibbs phenomenon, and discusses the non-convergence of the series even in the large limit (point convergence is guaranteed, but the curves do not have this feature). He points out...

That was my point; you never get the ideal. When properly measured with a scope, they look like the third picture you linked to. That is, they look like neither of the plots that I drew. They almost look like the approximate curve, which is due to bandwidth limitation caused by parasitic...

A seemingly good way to understand the overshoot and decay (ringing) of a square wave on a scope is that it is the result of bandwidth limiting. In that case, the Fourier series of a square wave \Pi(t) = \frac{1}{2 \pi} \sum_{n=-\infty}^\infty \frac{\sin(n \omega/2)}{n \omega/2} \exp(i n \omega...

ok, so the wrinkle is that J(r) gives information not just about current but about the phase of the current at that location, and that at a given r it is not the same at adjacent points. This is a result of dropping the time dependence out explicitly. Brilliant, thanks.

Good catch, you have identified my conceptual problem. When I start out, I have the Maxwell equations, namely \nabla \times \vec{H} = \vec{J} + \frac{\partial \vec{D}}{\partial t} \quad \quad \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} Then I write that...

This is driving me crazy. The derivation of the current distribution in a long cylindrical wire is extremely straightforward, giving J(r) = J(a) \frac{J_0(k r)}{J_0(k a)} where J is the current density, a is the radius of the wire, and k is the complex wave vector, which in a metal (with...

I agree that this is sound. Functionally, periodic BCs and vanishing at the boundary are equivalent. At that point, though, you've resorted to treating the spectrum as being due to a particle in a box. That is, without talking about a photon gas confined to a volume, you can't really get...

To my recollection, I've never seen a treatment of Debye theory that did not also invoke periodic boundary conditions to set the phonon wavelength with nodes at the boundaries. In many respects, the two are not very different. That's too bad, because invoking periodic boundary conditions in a...

Thanks for the reply. I think this forum is the closest, since it's the only one labeled for thermodynamics. I suppose the argument being made is that confining a gas of photons to a solid necessarily forces periodic boundary conditions, thereby constraining momentum so that standing waves...

It is perfectly possible to derive, for instance, the Maxwell distribution of speeds in a heuristic way with only two things: 1. The Gibbs hypothesis, which says that to count the number of states at speed v you take all the points in phase space between v and v+dv in velocity space. This...