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Hey all, does anyone know if it is possible (Yuichi?) if we can get copies of the solutions to the tests? There are some problems I am still not sure how to do, and it would be great if I could see how to them before the final.

Which problems are you having trouble with? Maybe some of us kind souls can help you out.

I noticed on the Wednesday wiki you had talked about test 1 and 3 being particularly useful. Yuichi does have the solutions for the first test on the downloads page, so you can get that at least.

And now, as you probably already know, he posted the rest of the solutions.

I'm curious what everyone put for #2 on quiz #4. I got full credit, but I don't feel like I deserved it; I only showed that <math>S^2 = S_x^2 + S_y^2 + S_z^2</math> with the new matrices, and I couldn't think of anything else to put. What other ideas were out there?

I showed that the <math>S_{\pm}</math> operators were different under the new definitions of <math>S_{x}</math> and <math>S_{y}</math>.

Students complaining about full credit. What IS this world coming to!

I showed the same thing as you Anaximenes. Based on the question, what more can you do? As long as you show something in the new system, you should get full credit. Hopefully we're that lucky on the final.

I assure you, I'm not complaining about getting full credit(=P), but I feel like I should be able to think of and show something more interesting that that.

I did the same as chavez.

Was it said whether the most recent chapters would be more of the material on the final or not? It the final based mostly on the more recent things, or it evenly spread between everything so far?or

The final will go up to chapter 5 section 1.

Forever yours,

Esquire

I think we actually go up through the Zeeman effect in chapter 6.

My impression however is that we should focus on the last part because the first few chapters build on themselves…. i.e. you can't do chapter 6 without knowing stuff from chapter 4 etc…

Are we going to have practice problems for the final?

In case you didn't see it yet, he posted a practice test.

The email we received said there will be a question closely related to the last discussion problem, so there is at least one question geared toward the end-of-semester material. It would also be conceivable to have a first-order perturbation problem also. Something like that could be tied into an older potential problem. I would guess we could solve for something like an infinite square well, then add a perturbation and solve for the new energies/wf's using our previously found energies/wf's.

Where is the final going to be? I think it's at 8:30 on Saturday, but I don't remember where it's going to be held.

Oh Joh04684, how could you forget. It'll be in Smith Hall 331 of course!

Oh yes, that's right…Thanks!

In strong-field zeeman effect, why is the total angular momentum not conserved, whereas Lz and Sz are?

When we consider the Zeeman effect, we take the magnetic field to be in the z-direction. The component of magnetic moment lying in the xy-plane experience a torque, which is the time derivative of angular momentum. If you have a non-zero time derivative, angular momentum must be changing.

The torque does not act upon the magnetic moment aligned with the z-direction., which explains why Lz and Sz are conserved.

Will we get an equation sheet for the final?

With all my heart,

Great Khan,

Esquire

Negative, sir!

Oh yea, I just read that in the email he sent.

Thanks!

Esquire

Oh Esquire – given your claim to world class style and charisma (being all that is man) I would have thought you'd be on top of this!

So, in a quantum system with discrete eigenvalues, are the expectation values always one of the eigenvalues? Is lack of sleep making the answer not obvious?

No, according to the textbook equation [3.49], <math> <Q>=\sum_n q_n |c_n| ^2 </math> The expectation value <math> <Q> </math> does not necessarily be one of the eigenvalues <math> q_n </math>.

Starting to get some questions and answers on the practice test and wondering how they compare…

#1 d) <math> L_x^2+L_y^2+L_z^2=L^2\\L_z=m\hbar \ \ \ L^2=\hbar^2l(l+1)\\L_x^2+L_y^2=L^2-L_z^2=2\hbar^2 \\</math> Is this the right approach?

That's the approach we took as well. We got the same answer.

That's what I got as well.

That's how I did it; couldn't really think of any other way.

me too.

On the discussion problem solutions, the first method used to calculate the parts of the matrix doesn't show how to get the off axis parts. Which way is this done? Or did I just miss something in the solutions? I know I can use the second way as well, but I'm curious as to the first method.

Nevermind, I got it. You just need to need use Psi 5 and Psi 6 instead of Psi 5 for both.

It's hard to understand the solution #3 of Quiz3.

For problem #3 of quiz 3, what you want to do is find relations between the cartesian coordinates and the polar coordinates because ∂/∂x can be rewritten as (∂r/∂x)∂/∂r+(∂θ/∂x)∂/∂θ+(∂φ/∂x)∂/∂φ and then you solve for ∂r/∂x, ∂θ/∂x, and ∂φ/∂x.

For example:

r²=x²+y²+z²

∂/∂x(r²)=∂/∂x(x²+y²+z²)

2r(∂r/∂x)=2x

∂r/∂x=x/r

and since x=rcosφsinθ,

∂r/∂x=cosφsinθ

and you just continue in this manner (helpful relationships: tanφ=y/x, cosθ=z/√(x²+y²+z²), x=rcosφsinθ, y=rsinφsinθ, and z=rcosθ).

we're only concerned about the r direction (Q=r∧p) so we're solving for

Q=x(∂r/∂x)∂/∂r+y(∂r/∂y)∂/∂r+z(∂r/∂z)∂/∂r

How does Griffths go from the 1st to the 2nd equation in equation 7.23 on page 301?

====Schrödinger's Dog 12/18====In equation 2.123 on page 72, why does the right hand side go to zero?

Hey, Cody and Jessica, guess who :P.

I seem to have forgotten this, how do you do 5.b in the final practice test?

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