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classes:2009:fall:phys4101.001:q_a_0928 [2009/09/28 03:05] – gebrehiwetclasses:2009:fall:phys4101.001:q_a_0928 [2009/09/30 10:55] (current) – myers
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-===== Sept 28 (Mon) Free particle and wave packet(?)=====+===== Sept 28 (Mon) SHO wrapping up, Free particle and wave packet=====
 **Return to Q&A main page: [[Q_A]]**\\ **Return to Q&A main page: [[Q_A]]**\\
 **Q&A for the previous lecture: [[Q_A_0925]]**\\ **Q&A for the previous lecture: [[Q_A_0925]]**\\
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 ===chavez 9:35 9/25=== ===chavez 9:35 9/25===
-Angular frequency for (deep) water waves is <math>\omega = \sqrt{\frac{g }{2}}</math> and the phase velocity is given by <math>v_{phase}=\frac{\omega}{k}=\sqrt{\frac{g}{2k}}</math>. The group velocity is given by <math>v_{group}=\frac{\delta\omega}{\delta k}=\frac{1}{2}\sqrt{\frac{g}{2k}}=\frac{v_{phase}}{2}</math>.+Angular frequency for (deep) water waves is <math>\omega = \sqrt{\frac{g k}{2}}</math> and the phase velocity is given by <math>v_{phase}=\frac{\omega}{k}=\sqrt{\frac{g}{2k}}</math>. The group velocity is given by <math>v_{group}=\frac{\delta\omega}{\delta k}=\frac{1}{2}\sqrt{\frac{g}{2k}}=\frac{v_{phase}}{2}</math>.
  
-==== Can 9:45 9/27 ====+=== Can 9:45 9/27 ===
 I didn't see the water wave problem on page 64, it is talking about the analytical methods. I didn't see the water wave problem on page 64, it is talking about the analytical methods.
 Anyway, a question for chavez, if <math>\omega = \sqrt{\frac{g }{2}}</math>, then shouldn't <math>v_{phase}=\frac{\omega}{k}=\sqrt{\frac{g}{2k^2}}</math>, is there a typo in the expression for the frequency somewhere? Anyway, a question for chavez, if <math>\omega = \sqrt{\frac{g }{2}}</math>, then shouldn't <math>v_{phase}=\frac{\omega}{k}=\sqrt{\frac{g}{2k^2}}</math>, is there a typo in the expression for the frequency somewhere?
 +
 +=== chavex 10:14 9/27 ===
 +Ah thanks for catching my mistake. It should have been <math>\omega = \sqrt{\frac{g k}{2}}</math>. I'll edit that into my original post.
  
  
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 === Blackbox - 23:49 - 09/27/09 === === Blackbox - 23:49 - 09/27/09 ===
 Yes, I had the same problem when I tried to calculate the expectation value in homework #1 and #3. For example, some of numerical integration can be solved by substituting "x^2" into "t" but some others are not easily done by integration rules. Should we memorize some specific integration results?  Yes, I had the same problem when I tried to calculate the expectation value in homework #1 and #3. For example, some of numerical integration can be solved by substituting "x^2" into "t" but some others are not easily done by integration rules. Should we memorize some specific integration results? 
 +
 +=== Esquire -10:54 09/30/09 ===
 +Here is a very nice site which discusses just about everything you need to know about the properties of the error function.
 +
 +[[http://functions.wolfram.com/GammaBetaErf/Erf/introductions/ProbabilityIntegrals/05/]]
  
 ==== Daniel Faraday 9/27 11am ==== ==== Daniel Faraday 9/27 11am ====
 Homework Question: on the question that's on the discussion sheet about energy scales in eV, what do we use for the size of the well for the neutron in the nucleus? Homework Question: on the question that's on the discussion sheet about energy scales in eV, what do we use for the size of the well for the neutron in the nucleus?
  
-==Schrodinger's Dog 9/27 2:07am==+===Schrodinger's Dog 9/27 2:07am===
 Well, I would guess the the rest mass of a neutron, but I was wondering what problem you are talking about? I didn't see this in our homework.  Well, I would guess the the rest mass of a neutron, but I was wondering what problem you are talking about? I didn't see this in our homework. 
  
-==Pluto 4ever 9/27 10:31pm==+===Pluto 4ever 9/27 10:31pm===
 If you are referring to the second half of the discussion problem then you just have to use the one half nanometer scale as it says in the problem. If you are referring to the second half of the discussion problem then you just have to use the one half nanometer scale as it says in the problem.
 +
 ====Hydra   9/27 11:00pm ==== ====Hydra   9/27 11:00pm ====
 Can somebody show me why the gaussian wave packet has the minimum uncertainty? It makes sense intuitively, I just want to see quantitatively. Can somebody show me why the gaussian wave packet has the minimum uncertainty? It makes sense intuitively, I just want to see quantitatively.
  
-==Schrodinger's Dog 9/27 3:03am== +===Schrodinger's Dog 9/27 3:03am=== 
-  Find <math>\sigma_x</math> and <math>\sigma_p</math>, multiply them together and you should get minimum uncertainty (i.e. <math>\frac{\hbar}{2}</math>. +Find <math>\sigma_x</math> and <math>\sigma_p</math>, multiply them together and you should get minimum uncertainty (i.e. <math>\frac{\hbar}{2}</math>). 
 + 
 +//**Yuichi**// You can check out section 3.5.2. 
 + 
 + 
 + 
 +==== time to move on ==== 
 + 
 + 
 +It's time to move on to the next Q_A: [[Q_A_0930]] 
 + 
 + 
 **Return to Q&A main page: [[Q_A]]**\\ **Return to Q&A main page: [[Q_A]]**\\
 **Q&A for the previous lecture: [[Q_A_0925]]**\\ **Q&A for the previous lecture: [[Q_A_0925]]**\\
 **Q&A for the next lecture: [[Q_A_0930]]** **Q&A for the next lecture: [[Q_A_0930]]**
  
classes/2009/fall/phys4101.001/q_a_0928.1254125139.txt.gz · Last modified: 2009/09/28 03:05 by gebrehiwet

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