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classes:2009:fall:phys4101.001:q_a_1028

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classes:2009:fall:phys4101.001:q_a_1028 [2009/10/29 10:48] – pmartinclasses:2009:fall:phys4101.001:q_a_1028 [2009/11/30 08:49] (current) – x500_bast0052
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 ===John Galt 1:12PM 10/28=== ===John Galt 1:12PM 10/28===
 Yes, I am on the same page with Mr. Faraday here. Class has been interesting and I previously thought going slower might be better, but it would be interesting to at least try it out at a faster pace and see what we think then. Yes, I am on the same page with Mr. Faraday here. Class has been interesting and I previously thought going slower might be better, but it would be interesting to at least try it out at a faster pace and see what we think then.
 +===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.
  
 +===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.
 +
 +
 +===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.
 +
 +===Devlin===
 +I also like the slower pace.  I think it gives me more time to fully understand the material.
 +
 +===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.
 +
 +===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.
  
 ====Anaximenes - 23:00 - 10/26/09==== ====Anaximenes - 23:00 - 10/26/09====
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 Does that help you gain an intuitive/qualitative understanding?  (I obviously wasn't anything like rigorous, but sometimes that's ok.) Does that help you gain an intuitive/qualitative understanding?  (I obviously wasn't anything like rigorous, but sometimes that's ok.)
 +
 +===Yuichi===
 +I think the physics lies in the fact that operators such as "x," "d/dx" and their mixtures represent physically observable quantities in QM.  Combining this fact (speculation?) with the fact that "x" and "d/dx" don't commute (and as a result, their combinations don't often commute) lead to the uncertainties between those quantities whose operators don't commute.  I guess once this starting point is set, you can say that the remaining steps do not involve much physics.
  
 ==== joh04684 10/27 10:47 PM ==== ==== joh04684 10/27 10:47 PM ====
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 Ker(H-E*I)≠{0},  Ker(H-E*I)≠{0}, 
 which means that the matrix H-E*I fails to be invertible, which can also be stated by saying  which means that the matrix H-E*I fails to be invertible, which can also be stated by saying 
-det(H-E*I)=0</math>, +det(H-E*I)=0, 
 which is the determinate you are referring to. which is the determinate you are referring to.
 By Ker (kernal) of a matrix H-E*I=A, or any transformation, I mean the set of solutions to A<math>|v></math>=0. From the fact that E is an eigenvalue of H, we know that <math>|v></math> exists and that it is nonzero. By Ker (kernal) of a matrix H-E*I=A, or any transformation, I mean the set of solutions to A<math>|v></math>=0. From the fact that E is an eigenvalue of H, we know that <math>|v></math> exists and that it is nonzero.
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 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!
  
-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>
  
-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>
  
 "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>.
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 ===Pluto 4ever 10/28 10:50PM=== ===Pluto 4ever 10/28 10:50PM===
 I just thought it would be <math><\Psi_n|\Psi></math>. Then again, I could be wrong. I just thought it would be <math><\Psi_n|\Psi></math>. Then again, I could be wrong.
 +=== 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?
 +===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>
  
 +===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?
  
 ====Links==== ====Links====
classes/2009/fall/phys4101.001/q_a_1028.1256831300.txt.gz · Last modified: 2009/10/29 10:48 (external edit)

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