Recent content by crossword.bob

Sorry, I’ve now seen that this is a known thing. I’ll work on my search-fu.

In Compton's 1923 paper on X-rays scattering from light elements, he presents the following diagram: Here, ## h\nu_0/c ## is the momentum of the incident photon, ## h\nu_\theta/c ## is that of the scattered photon and ## mv/(1-\beta^2)^{1/2} ## is that of the recoiled electron. He uses this to...

I’m currently reading it, as it seems to cover exactly what I’m looking for. But I’m struggling with some of his ‘counting’ in the early chapters. E.g., in section 1.7, he derives the four connected components of the Lorentz group, based on the free selection of two signs. That’s fine. But for...

Yes, pretty much, though it depends on state. Molecules/atoms can have a number of degrees of freedom within a system. For example, in a gas made up of diatomic molecules, each molecule will have six degrees of freedom: Three degrees of freedom from translational velocity of its centre of mass...

I’ve been self-studying quantum mechanics for a while, and currently looking at scattering theory, using chapters in books by Shankar, Sakurai, and John R. Taylor’s Scattering Theory text. But was wondering if there are any good sources that relate the theory in these books to actual experiments...

Interesting. I can see in your derivation of the photoelectric effect that the delta function arises from \sin^{(2)}(Tx)/x^{(2)} as T\rightarrow\infty. In the text, the quoted result comes from an integral like $$\int \frac{\sin^2[(E_m-E_n)T/2\hbar]}{(E_m-E_n)^2}\,dE_m,$$ and noting that...

I’m currently self-studying from Feynman & Hibbs Quantum Mechanics and Path Integrals, but having trouble with a statement in the chapter on time-dependent perturbations. Background: They define $$V_{mn}(t_c) = \int_{-\infty}^\infty \phi_m^*(x_c)V(x_c,t_c)\phi_n(x_c)\,dx_c,$$ where V(x,t) is...

Thanks, that helps. I suspect it will take a little time for me to fully digest that paper, but there is some solace is knowing the problem that’s been bothering me has bothered better minds than mine in the past!

Most textbooks include an example of entropy of mixing that involves removing a partition between two (in principle) distinguishable gases, and compare this to the case where the two gases are indistinguishable. What I’ve not yet been able to figure out is what the consequences of this...

I'm currently working (slowly) through Goldstein (et al), 3rd Edition, and a remark in the section on Action-angle Varibles for Completely Separable Systems (10.7) is giving me pause. We're told that the orbit equations for all ##(q_i, p_i)## pairs in phase space describe libration or periodic...

In a loose sense, treating time as a fourth dimension, and disregarding curvature for now (so SR), everything is always moving at a constant speed—the speed of light. If you are at rest in a given frame, then in that frame, 100% of your motion is along the time axis. Now, say you start...