===== Dec 19 (Sat) Final Exam ===== **Return to Q&A main page: [[Q_A]]**\\ **Q&A for the previous lecture: [[Q_A_1219]]** **If you want to see lecture notes, click [[lec_notes]]** **Main class wiki page: ** [[home]] --------------------------------------- ====John Galt 12/16==== 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. ===chavez 6:40 12/16=== Which problems are you having trouble with? Maybe some of us kind souls can help you out. ===The Doctor 12/16=== 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. ===The Doctor 12/17=== And now, as you probably already know, he posted the rest of the solutions. ====Anaximenes - 18:00 - 12/16/09==== 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 S^2 = S_x^2 + S_y^2 + S_z^2 with the new matrices, and I couldn't think of anything else to put. What other ideas were out there? ===chavez 6:40 12/16=== I showed that the S_{\pm} operators were different under the new definitions of S_{x} and S_{y}. ===Spherical Chicken.=== Students complaining about full credit. What IS this world coming to! ===poit0009 12:40 12/17=== 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. ===Anaximenes - 15:20 - 12/17/09=== 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. ===Devlin 12/18=== I did the same as chavez. ====The Doctor 12/16==== 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 Esquire 12/16 (age of the forgotten)=== The final will go up to chapter 5 section 1. Forever yours, Esquire === joh04684 12/16 === I think we actually go up through the Zeeman effect in chapter 6. === Spherical Chicken stardate 191933.4 == 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... === Blackbox 12/16 === Are we going to have practice problems for the final? ==The Doctor 12/17== In case you didn't see it yet, he posted a practice test. ===poit0009 12:43 12/17=== 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. ==== joh04684 12/17 ==== 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. === Spherical Chicken === Oh Joh04684, how could you forget. It'll be in Smith Hall 331 of course! === joh04684 12/17 === Oh yes, that's right...Thanks! ==== liux0756 12/17 ==== In strong-field zeeman effect, why is the total angular momentum not conserved, whereas Lz and Sz are? ===poit0009 12:51 12/17=== 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. ====Esquire 12/17 (Age of Locking the Wiki)==== Will we get an equation sheet for the final? With all my heart, Great Khan, Esquire === joh04684 12/17 === Negative, sir! === Esquire 12/17 (Age of Course)=== Oh yea, I just read that in the email he sent. Thanks! Esquire === Spherical Question 12/17 === 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! ==== Daniel Faraday & Captain America 12/18 3pm (Age of What is the Deal with that Esquire guy?)==== 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? ===liux0756 12/18 3pm=== No, according to the textbook equation [3.49], =\sum_n q_n |c_n| ^2 The expectation value does not necessarily be one of the eigenvalues q_n . ==== Super Hot Guy 12/18 not late yet ==== Starting to get some questions and answers on the practice test and wondering how they compare... #1 d) 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 \\ Is this the right approach? ===Captain America and Daniel Faraday 12/18 almost late yet=== That's the approach we took as well. We got the same answer. ===Devlin 12/18=== That's what I got as well. === Mercury 12/18 === That's how I did it; couldn't really think of any other way. ===Andromeda=== me too. ====The Doctor 12/18==== 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. ===The Doctor 12/18=== Nevermind, I got it. You just need to need use Psi 5 and Psi 6 instead of Psi 5 for both. ====Blackbox 12/18==== It's hard to understand the solution #3 of Quiz3. === Mercury 12/18 === 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 ====Schrödinger's Dog 12/18==== How does Griffths go from the 1st to the 2nd equation in equation 7.23 on page 301? ===The Doctor 12/18=== Consider the first term of the 2nd equation: (r_1+r_2) Square it and you get (r_1^2+r_2^2+2 r_1 r_2) So if you take the square root of that you get back to where you started. This square root is what happens in going from the first to the second equation for the first term, but the idea is the same for the second one as well. ====Schrödinger's Dog 12/18==== In equation 2.123 on page 72, why does the right hand side go to zero? ===The Doctor 12/18=== As he said it's a sliver with infinitely small width and finite height. If it was infinite height the area would still have to be taken into account, but it's not in this case. ====Schrödinger's Dog 12/18==== Hey, Cody and Jessica, guess who :P. ====Andromeda==== I seem to have forgotten this, how do you do 5.b in the final practice test? ===The Doctor 12/18=== Someone correct me if I'm wrong, but I believe you're just expecting plus and minus hbar as your possible values and you just normalize the a and b elements of the spinor to give you the probability of each. ==The Doctor 12/18== Unless this doesn't work for S_y . == Zeno 12/19 12AM == Pages 174 and 175 go over the solution strategy for S_x which is very similar for S_y. For part a, did anyone else get plus and minus h-bar over 2 with probabilities 5/9 and 4/9? Good luck tomorrow (or today) everybody. ==== Zeno 12/18 11PM ==== Is anyone else embarrassed for not getting question 3 right on quiz 4 after seeing the solution? It seemed incredibly difficult when taking the exam, but it seem so simple redoing it... Also, I think the practice exam look deceptively easy. I can work these solutions out on the spot without referencing the book or anything, but I have the feeling that the exam questions are going to be much harder... or at least conceptually challenging. My problem on the exams (and the homework, for that matter) has always been interpreting the problem correctly. If given enough time I think I can solve just about anything. ====The Doctor 12/18==== What are people doing for the 4th question on the practice final? Is it actually really easy or am I'm thinking about this wrong? ===Anaximenes - 00:40 - 12/19/09=== Near as I can tell, it should just be \psi_a (x_1)\psi_b (x_2) - \psi_b (x_1)\psi_a (x_2). Is that what you were thinking? Or do you think the problem wants us to multiply in the spin wavefunction? E.g., \psi_a (x_1)\psi_b (x_2)[\chi_+ (x_1) \chi_- (x_2) - \chi_- (x_1) \chi_+ (x_2)]? (I'm not especially certain that expression actually means anything.) ====Esquire 12/19 (Age of Final)==== What did you guys think about the final? I thought it wasn't terrible, thought I didn't get a few things. ===Anaximenes - 15:30 - 12/19/09=== I thought it was good. All of it was reasonable (not incredibly easy or difficult), but it covered a wide range of topics. What did everyone put for #6? Those open-ended questions always take me the longest. I described how the graph shows the Zeeman effect is dominant at high \beta but Fine Structure is dominant at low \beta; that of the 8 energy eigenvalues, 4 had simultaneous eigenstates of j, j_z, m_l, and m_s; and that the two middle eigenvalues have \displaystyle \lim_{\beta \rightarrow \infty} \lambda = -3\gamma (i.e., they become degenerate). === Blackbox 12/19 === I'm just wondering whether these kinds of questions and answers or opinions about the exams are also counted in the total. ====Links==== --------------------------------------- **Return to Q&A main page: [[Q_A]]**\\ **Q&A for the previous lecture: [[Q_A_1219]]**