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| classes:2009:fall:phys4101.001:q_a_1028 [2009/10/29 21:42] – x500_voukx002 | classes:2009:fall:phys4101.001:q_a_1028 [2009/11/30 08:49] (current) – x500_bast0052 |
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| ===Hydra 9PM 10/29=== | ===Hydra 9PM 10/29=== |
| I agree that it seems to be dragging a bit, but perhaps it's for our own good? I think Yuichi is drilling us now so that when we reach chapter 4 we won't be so lost in the notation. | I agree that it seems to be dragging a bit, but perhaps it's for our own good? I think Yuichi is drilling us now so that when we reach chapter 4 we won't be so lost in the notation. |
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| | ===Dark Helmet 10/29=== |
| | It seems to be for our own good to me too. I know i, at least, gained a more deep-seated understanding by the slower pace and review. |
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| | ===Captain America 10/30 10:10AM === |
| | Slow is good now. If you look later on in the book we will be needing to use all of this notation to solve non-trivial problems. If we don't completely understand everything in class right now, we won't be able to use it in the future. We really need to get this solid base down first. |
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| | ===Devlin=== |
| | I also like the slower pace. I think it gives me more time to fully understand the material. |
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| | ===Hardy 11/01 10:10AM === |
| | Actually, I appreciate the slow pace that help me understand a lot though Anaximenes's concern also bothers me. I think it will be better to separate the 50 minutes into two parts. We can cover the materials faster in one part and review important concepts and make us surely understand them in the other part of time. |
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| | ===Esquire 11/02 2:00PM=== |
| | The pace seems a bit slothish for me as well. Specifically It seems unnecessary to spend sizable portions of class deciding on what to discuss. |
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| ====Anaximenes - 23:00 - 10/26/09==== | ====Anaximenes - 23:00 - 10/26/09==== |
| I'm trying to make sense of how the different "spaces" are represented in short-hand. Correct me if I'm wrong! | I'm trying to make sense of how the different "spaces" are represented in short-hand. Correct me if I'm wrong! |
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| Energy space <math>C_n</math> in short-hand is <math><f_n|\Psi></math>. (by equation [3.46]) | Energy space <math>c_n</math> in short-hand is <math><f_n|\Psi></math>. (by equation [3.46]) With <math>c_n=f_n(x)</math> |
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| Momentum space <math>\Phi(p,t)</math> in short-hand is <math><f_p|\Psi></math>. (by equation [3.53]) | Momentum space <math>\Phi(p,t)</math> in short-hand is <math><f_p|\Psi></math>. (by equation [3.53]) With <math>f_p=\frac1 sqrt{2\pi\hbar}exp(\frac{-ipx} {\hbar})</math> |
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| "Real" space <math>\Psi(x,t)</math> I'm not sure about. Is it simply: <math>|\Psi></math> or in terms of <math>\Phi</math> and equation [3.55] I get a short-hand of <math><f_p|<f_p|>></math>. | "Real" space <math>\Psi(x,t)</math> I'm not sure about. Is it simply: <math>|\Psi></math> or in terms of <math>\Phi</math> and equation [3.55] I get a short-hand of <math><f_p|<f_p|>></math>. |
| === Yuichi === | === Yuichi === |
| As Eqn 3.52 implies, the equivalent to the real-space eigenfunction of operator <math>\hat x</math> is <math>\delta(x-y)</math> where //x// represents the variable that <math>\psi(x)</math> is expressed in so that one can write <math><g_y|\psi></math> as <math>\int \delta(x-y)\psi(x) \mathrm dx</math>, while //y// is the eigenvalue of the position eigenfunction <math>\delta(x-y)</math>. //i.e.// <math>{\hat x}\delta(x-y) = y\delta(x-y)</math>. Now you can get <math>c_y</math> in the same way as <math>c(p)</math> or should we have written as <math>c_p</math> for a consistency? | As Eqn 3.52 implies, the equivalent to the real-space eigenfunction of operator <math>\hat x</math> is <math>\delta(x-y)</math> where //x// represents the variable that <math>\psi(x)</math> is expressed in so that one can write <math><g_y|\psi></math> as <math>\int \delta(x-y)\psi(x) \mathrm dx</math>, while //y// is the eigenvalue of the position eigenfunction <math>\delta(x-y)</math>. //i.e.// <math>{\hat x}\delta(x-y) = y\delta(x-y)</math>. Now you can get <math>c_y</math> in the same way as <math>c(p)</math> or should we have written as <math>c_p</math> for a consistency? |
| | ===Green Suit 10/30=== |
| | So the position measurement of <math>x</math> in the "real" space <math>\Psi(x,t)</math> in short-hand is <math><g_y|\Psi></math> (by equation [3.52]) With <math>g_y=\delta(x-y)</math> |
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| | ===Pluto 4ever 10/31 2:55PM=== |
| | Does <math>g_y</math> or <math>\delta(x-y)</math> have to be normalized for this to work? |
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| ====Links==== | ====Links==== |