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| classes:2009:fall:phys4101.001:q_a_1009 [2009/10/11 21:43] – yk | classes:2009:fall:phys4101.001:q_a_1009 [2009/10/22 12:21] (current) – czhang |
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| ===David Hilbert's Hat 10/10 9:20am=== | ===David Hilbert's Hat 10/10 9:20am=== |
| I think Griffiths makes a reference to the delta function when it's used as a distribution of a point particle's mass/charge. Everywhere that's not located at the particle it's zero, but at the particle it's infinity; when you integrate over all space it comes out to be 1, because you have one particle. That seems to be the easiest way to see the delta function - it is very peculiar because it is zero everywhere except at one point it's infinity, but it integrates to 1, like a point particle's distribution (which seems a lot more familiar). | I think Griffiths makes a reference to the delta function when it's used as a distribution of a point particle's mass/charge. Everywhere that's not located at the particle it's zero, but at the particle it's infinity; when you integrate over all space it comes out to be 1, because you have one particle. That seems to be the easiest way to see the delta function - it is very peculiar because it is zero everywhere except at one point it's infinity, but it integrates to 1, like a point particle's distribution (which seems a lot more familiar). |
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| ==== Anaximenes - 22:30 - 10/09/09 ==== | ==== Anaximenes - 22:30 - 10/09/09 ==== |
| This question is about problem 2.34. The problem asks us in part c to show that <math>T=\sqrt{\frac{E-V_0}{E}}\frac{|F|^2}{|A|^2}</math>. However, Eq. 2.139 on page 75 says <math>T\equiv \frac{|F|^2}{|A|^2}</math>. That's with three lines, as in identically equal, as in any statement that they're not equal (such as that in the prompt in 2.34c) is incongruent. Now, I remember the professor said in class that <math>T=\frac{|F|^2}{|A|^2} \frac{k_2}{k_1}</math>, but how do we //show// that? We have no definition of T other than the (patently false) one in 2.139. For shame, Griffiths. For shame. | This question is about problem 2.34. The problem asks us in part c to show that <math>T=\sqrt{\frac{E-V_0}{E}}\frac{|F|^2}{|A|^2}</math>. However, Eq. 2.139 on page 75 says <math>T\equiv \frac{|F|^2}{|A|^2}</math>. That's with three lines, as in identically equal, as in any statement that they're not equal (such as that in the prompt in 2.34c) is incongruent. Now, I remember the professor said in class that <math>T=\frac{|F|^2}{|A|^2} \frac{k_2}{k_1}</math>, but how do we //show// that? We have no definition of T other than the (patently false) one in 2.139. For shame, Griffiths. For shame. |
| I may have made some mistakes like where 2pi goes, so please carefully check if you are interested in this issue. | I may have made some mistakes like where 2pi goes, so please carefully check if you are interested in this issue. |
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| | === Can 10/21 10:52am === |
| | For Yuichi, instead of saying A^2 is probability, I think it would make much more sense if we think of A^2 as incident intensity, just my personal opinion not sure if it is rigorous. Recall that the square of the amplitude of for E field is proportional to the intensity , E^2 is proportional to I, same analogy can be made here, then the probability can be interpreted as transmitted intensity versus incident intensity. <math>T=\frac{F^2}{A^2}</math>. At least, I think this might be easier to understand transmission intuitively, maybe not mathematically, one still has to work out all the math. |
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| | ====Liam Devlin 10/12, 10:45am==== |
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| | Why is k a known for a scattering problem? |
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| | ===Can 10/22 12:15pm === |
| | Since for scattering problem <math>E=\frac{h^2k^2}{2m}</math> which means <math>k=\frac{\sqrt{2mE}}{h}</math>, and E is the incident energy of the particle, which can be manually tuned. E is known , so k is known. |
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| | ====Aspirin 10/12, 2:30pm==== |
| | Why does the coefficient, D, of the genernal solution which is <math> \psi_I_I = C e^{ikx} + D e^{-ikx} </math> cancel out? |
| | Yuichi mentioned the reason, but I didn't fully get it. |
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| | ===Blackbox 10/12, 3:20pm=== |
| | I'm not quite sure I understood that correctly, but if I say, when a particle moves from the left to the right direction, it will transmitt through the Delta function well. In other words, there is no physical values from the right to the left direction. If we think of the opposite situation, a particle moves from the right to the left, in the first region, <math> \psi_I = Ae^{ikx} + Be^{-ikx} </math>, A would be removed because nothing can go back to the right direction. |
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| | ====Blackbox 10/12, 6:00pm==== |
| | I might write wrong in my note though. On last Wednesday, Yuichi mentioned the unit of α is Energy/length. Isn't it Energy*length? |
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| ====Links==== | ====Links==== |