Net Angular Momentum: Clarifying Confusion

[cooev769]

Really don't like this book, he's crazy ambiguous, I've looked it up myself on the internet and it makes far more sense, but it's our textbook so I have to understand what he's trying to say.

We're coupling the angular momentum of an electron's orbital and spin based angular momentum. And he says verbatim:

"If a hydrogen atom is in the state, l,m,n, the net angular momentum of the electron (spin+orbital) is l+0.5, l-0.5"

So I have no idea if he's talking about in the Z component, the squared, or what, he also doesn't say that he's omitted the h units, I only know that those are the units from other textbooks, also it would seem he is talking about the quantum number j, not actually the total angular momentum, which he hasn't actually explained. So I have no idea what he is talking about.

If he is talking about the z component well Lz on the state would be mh wouldn't it, and then Sz would also be mh. So the total would be 2mh, he's clearly not talking about this.

So i figured he must be talking about the quantum number, which he hasn't explained at all I had to research to find:

j = l +/- s

But then he goes on to say if we add in the proton, we get, l+1, l or l-1. But if he is indeed talking about the quantum number j, then you only get:

j = l + 1, l - 1, 0

So am I right to assume he's talking about the quantum number total angular momentum, and not actually adding the angular momenta from orbit and spin and getting the number l+0.5 and l-0.5

Please clarify this. Thanks.

 

[cooev769]

I mean it would be true that the angular momentum is l+0.5, on the top rung if the two are aligned so to speak, and l-0.5 if the two are antiparallel so to speak, but there are so many potentials in between depending on l, and he hasn't talked about this at all or explained what the hell he is talking about.

 

[MisterX]

I mean it would be true that the angular momentum is l+0.5, on the top rung if the two are aligned so to speak, and l-0.5 if the two are antiparallel so to speak, but there are so many potentials in between depending on l...

$j = \ell + 1/2$ and $j = \ell - 1/2$ are the only two values for definite $j$. Addition of angular momentum should be covered in any decent QM textbook.

You can look at the section beginning on page 151 here
http://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf

 

[cooev769]

Yes but is this a quantum number or is this the actual total angular momentum values, that is what is not made explicit in this textbook.