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| classes:2009:fall:phys4101.001:quiz_3_1113 [2009/11/11 08:53] – x500_bast0052 | classes:2009:fall:phys4101.001:quiz_3_1113 [2009/11/13 09:23] (current) – x500_maxwe120 |
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| ===Devlin=== | ===Devlin=== |
| This might be naive, but I think just a general understanding of what they do and how they act should suffice. In lecture yesterday (or monday maybe?), he spent a lot of time on the Bessel function graph. I think he wants us to really understand what the graph means and why it acts that way. | This might be naive, but I think just a general understanding of what they do and how they act should suffice. In lecture yesterday (or monday maybe?), he spent a lot of time on the Bessel function graph. I think he wants us to really understand what the graph means and why it acts that way. |
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| | ===Hydra 11/11 4pm=== |
| | Making that equation sheet made me worry even MORE about the test... The most important equations , I felt, were the results of tedious derivations. These main equations were fairly large (larger than I could memorize with ease)... So I am wondering how Yuichi is going to approach writing this test? Obviously everybody has opinions about which equations were "most important" so asking a question stemming from an important equation, say 4.63, is either hit or miss. If you have the right equation you'd be in luck, but if not, it'd be painful to know that 20 (or even 40!) points is swirling down the toilet.... |
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| | SOO long story short, I know Yuichi doesn't want to write a test where a few lucky people wrote down the right equation. I'm thinking everything we need will be given in the test problem, and we will be asked to build off of it with the methods learned in lecture & discussion. Something along the lines of today's lecture (writing out the basic steps taken to find equations for the radial wave function.) |
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| | I'm worried because it feels like I'm throwing away a bulk of the chapter's equations, just to commit to understanding the basic methodology of "how-to-get-there" Yikes! Is this a fast track to nowhere? |
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| | ===chap0326 11/12 13:39=== |
| | I wouldn't be too worried. The derivations Griffiths did, he pulled a bunch of definitions out of nowhere that were pretty arbitrary unless you already knew what you wanted to get. So I would be surprised if we were expected to pull that sort of stuff out of the ether. |
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| | ===physics4dummies 11/12 8:30pm=== |
| | Been doing the practice test and I need to know if problem 2 is as easy as plugging the change of coordinates into the operator equation. |
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| | ==Zeno 9am 11/13== |
| | Generally, yes, but since the x and y momentum operators involves derivatives of x and y respectively you need to change the derivatives from Cartesian to spherical coordinates. You can do this by exploiting the chain rule for derivatives and obtaining |
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| | <math>\frac{\partial}{\partial x}= \frac{\partial \rho}{\partial x} \frac{\partial}{\partial \rho} + |
| | \frac{\partial \theta}{\partial x} \frac{\partial}{\partial \theta} + |
| | \frac{\partial \phi}{\partial x} \frac{\partial}{\partial \phi} </math> |
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| | Then just use the definitions for the change of coordinates to compute each respective component derivative and you'll be left with spherical coordinate derivative operators multiplied by variables on to the left. If you do it correctly you'll obtain equation 4-129. |
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| | ===Ekrpat 1135=== |
| | Doing problem 3.38 for review, part b for A, I get <math><A> = \lambda (c_1*c_2 + c_2*c_1 + 2|c_3|^2)</math>. Is it possible to cancel the <math>c_1*c_2</math> and <math>c_2*c_1</math> terms by kroenecker delta leaving <math><A> = (2\lambda|c_3|^2)</math>? Thanks! |
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| | ==chap0326 11/12 23:15== |
| | I'm not sure that you can. I think when Griffiths proved that in chapter 2.2, he used two different states of wave function, but the c's {<math>(c_1*c_2 + c_2*c_1 + 2|c_3|^2)</math>} are, I think, more like dimensions of a single state rather than different states. |