Recent content by jmcelve

The problem is that you're applying classical electromagnetism to a particle that doesn't behave classically. Hopefully someone who knows QED will step in at this point and maybe elaborate a little, but I can't really give a deeper reason than that at the moment.

No, it doesn't imply that. Precisely. For the electron to be at rest, it would necessarily have a well-defined position (x=x_rest). But it must also necessarily have a well-defined momentum since it is at rest (v=0), and this violates the uncertainty relation.

Spin is a quantum mechanical phenomenon. It doesn't have a classical analogue, so you can't treat the electron as if it's rotating. In fact, if we naively treated the angular momentum classically, we'd find that the electron (if it were spherical) would have a tangential velocity many times the...

Sure, and that's the whole point. There is a *phase* by which they differ, though the *amplitudes* of these particular plane waves are equal. In particular, their phases differ such that they propagate in opposite directions (+x and -x).

Well, you agree that, in general, complex exponentials with the same coefficients differ only by a phase factor, yes? If so, then surely you can see how this is simply a particular case of that general rule.

To expand on vanhees's statement a bit, when we say "completeness," we are talking about a basis (usually an eigenbasis of a self-adjoint operator) for a particular vector space V. If we have a complete basis for a particular space (in this case, |i\rangle collectively spans the vector space V)...

We denote it that way because we've chosen to project the eigenstates and the operators in terms of \theta and \phi. We could equally express the eigenstates |l, m \rangle and the operators \hat{L^{2}} and \hat{L_{z}} in terms of Cartesian coordinates. We express the eigenstates in the standard...

Hi aaaa202, The "discreteness" of QM is actually manifest in potentials. It is not the case that "all energies are quantized" since it is boundary conditions that demand that certain eigenfunctions (and consequently certain energies) be solutions to the Schrodinger equation for particular...

Yeah, that's it HallsofIvy. For some reason, I had the impression I was supposed to do a full contour integral. On a second glance, I realized I had completely misread the problem. Shows the value of reading comprehension in mathematics! Thanks for the help.

Hi everyone, I'm trying to work out the integral of 1/z over the path (0, -i) to (-i, a) to (a, i) to (0, i) for a any real number greater than 0. I'm having trouble trying to determine what to do at z=0 since the integral doesn't exist here. Any ideas as far as how to push forward? My...

It's nice to see that there's still some uncertainty (!) regarding these questions. I don't feel so alone in pondering them now. :smile: I'll have to consider what you've said more thoroughly, Naty1, but thank you for the response. The same thanks go to you Jano, though I think Naty1 is...

Hi everyone, I know this topic has been discussed quite a bit -- and in particular it's been done in this thread and this thread. But there are still some things I want to talk about in order to (hopefully) clarify my own thoughts. One of the threads discusses this Ballentine article in which...

Noted. Thanks for the help.

That's super ugly. We really only talked about expanding epsilons in terms of deltas when there were four differing indices, not six. Is there a method to do this problem that requires using only four indices?

Determining the commutation relation of operators -- Einstein summation notation Homework Statement Determine the commutator [L_i, C_j] . Homework Equations L_i = \epsilon_{ijk}r_j p_k C_i = \epsilon_{ijk}A_j B_k [L_i, A_j] = i \hbar \epsilon_{ijk} A_k [L_i, B_j] = i \hbar...