Recent content by Albereo

Ah, got it! So then the expectation value for the z-component is straightforward, as well as the one for ##L##^{2}. But I can't do the same thing for ##L##_{x} because the state isn't an eigenfunction of that operator. Do I then turn to the commutation relations?

Thanks for all your help so far. This isn't coursework, so perhaps I'll look up the conventions later and just pick my ordering for the moment. So with that written for the state, to find the expectation values, I'd have to do <##L##_{z}> = <\Psi|\frac{h}{i}\frac{\partial}{\partial...

Okay, the Dirac notation is definitely one spot where I'm a bit fuzzy. But I think it would be something like: \Psi=\frac{1}{\sqrt{26}}|1, -1> + \frac{4}{\sqrt{26}}|1, 0> - \frac{3}{\sqrt{26}}|1, 1> But is the ordering of states important here? (If this is correct)?

Oops, I meant |1, 1>.

I've got a linear combination of the states |##l## , ##m##_{l}> = |1, -1>, |1, 0>, and |0, 1>. Do I now need to determine the coefficients, or do I proceed some other way?

Consider a quantum system with angular momentum 1, in a state represented by the vector \Psi=\frac{1}{\sqrt{26}}[1, 4, -3] Find the expectation values <L_{z}> and <L_{x}> I'm reviewing my quantum mechanics; I had a pretty horrible course on it during undergrad. I feel like this should be...

I recently read somewhere that the predictions of QED in the classical limit haven't been nearly as well-studied as, say, the classical limit of quantum mechanics. This is a little confusing: doesn't QED just reduce to Maxwellian electrodynamics with additional small nonlinear quantum...

I haven't seen that alternative notation before, are there any advantages (besides the avoidance of hand-cramps from writing indices) to using it? Also, can it be used easily instead of the usual notation in QFT and GR?

Ah, thanks! Index gymnastics...going to be fumbling with those for a while.

This isn't actually coursework, I'm doing some studying on my own. These are my very preliminary attempts to wrangle with tensor notation, so please be patient with me. I'm trying to get the components of the electromagnetic field tensor from \partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu} But...

Hey I haven't read through all 8 pages of the replies so forgive me if this has come up before. In your "Undergraduate Preparation" section you note that a student should have working knowledge of two programming languages, minimum, and recommend that these are Fortran and C. I think this needs...

Oh! I get it now. Thanks a bunch, you've cleared up all my confusion with when factors are needed.

Problem Statement: I'm having some trouble understanding how to write charge densities using delta functions, particularly when they involve geometries other than Cartesian. So I have a disk moving with velocity v (along the z-axis) that has total charge Q, and I'm trying to write ρ(x,t) so that...

As is the same with my institution. However, some schools actually have separate departments, or at least separate emphases, for "pure" math versus applied math. Applied math puts more of an emphasis on those fields which are relevant to forming the theoretical backbone of the various sciences...

YES. Don't listen to the pretentious people here telling you that pure math is true and difficult and everything else is book-keeping. Here's the thing: your abilities to be a good student have nothing to do with your intellectual capabilities, creativity, or ingenuity. Some of the most...