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classes:2009:fall:phys4101.001:q_a_1214

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classes:2009:fall:phys4101.001:q_a_1214 [2009/12/16 00:03] – elyclasses:2009:fall:phys4101.001:q_a_1214 [2009/12/19 16:42] (current) – x500_sohnx020
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 ===chavez 09:32 12/12=== ===chavez 09:32 12/12===
 I just showed that operating <math>L_{z}</math> on <math>\psi</math> was equivalent to multiply <math>\psi</math> by a constant <math>\lambda</math>. I just showed that operating <math>L_{z}</math> on <math>\psi</math> was equivalent to multiply <math>\psi</math> by a constant <math>\lambda</math>.
 +
 +==Dark Helmet 12/15===
 +I could not think at all what to do for number one.  What it was asking was so short and simple i just had no idea how to accomplish it.
  
 === Zeno 12/14 9AM === === Zeno 12/14 9AM ===
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 ===nikif002 2:10 PM 12-15=== ===nikif002 2:10 PM 12-15===
 I am pretty sure Chavez and Zeno have it right - it's the definition of an eigenvalue, after all. What I did was convert the WF from polar to Cartesian coordinates, then operate <math>xp_y-yp_x</math> on it. You should then get a result that is a constant multiplied by the Cartesian form of the WF found earlier. I am pretty sure Chavez and Zeno have it right - it's the definition of an eigenvalue, after all. What I did was convert the WF from polar to Cartesian coordinates, then operate <math>xp_y-yp_x</math> on it. You should then get a result that is a constant multiplied by the Cartesian form of the WF found earlier.
 +
 +===prest121 6:00pm 12/16===
 +All you had to do for #1 was know that <math>L_z = -i\hbar \frac{\partial}{\partial\phi}</math>.  Thus, <math>L_z\varphi = L_z(e^{i\phi}) = -i\hbar \frac{\partial}{\partial\phi}(e^{i\phi}) = \hbar(e^{i\phi}) = \hbar\varphi</math>.  This is the definition of an eigenvalue.
  
 ===Dark Helmet 12/15 12:00=== ===Dark Helmet 12/15 12:00===
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 ===Dark Helmet 12/15 12:00=== ===Dark Helmet 12/15 12:00===
 Is it all of 6?  Or just some sections? Is it all of 6?  Or just some sections?
 +
 +===Yuichi===
 +This kind of forum does not seem a good way to pin down this type of info.  Misinformation seems to go around and around.
 +
 +Setion 5.1 WILL BE included in the final, though 5.2 and later sections won't be.
 +
 +Hyperfine structure will also be excluded from Chap. 6.
 +
  
 ====Blackbox 12/15==== ====Blackbox 12/15====
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 ===Pluto 4ever 12/15=== ===Pluto 4ever 12/15===
 I'm not entirely sure, but I think it means where the states are eigenfunctions of <math>J_z</math>, <math>L_z</math>, and <math>S_z</math>. I'm not entirely sure, but I think it means where the states are eigenfunctions of <math>J_z</math>, <math>L_z</math>, and <math>S_z</math>.
 +==Yuichi==
 +Think again.
 ===Andromeda 12/15/09 8pm=== ===Andromeda 12/15/09 8pm===
 i thought it meant states(combination of vectors) that will give you a diagonal matrix at the end instead of states that will have off-diagonal parts as well. not sure though! i thought it meant states(combination of vectors) that will give you a diagonal matrix at the end instead of states that will have off-diagonal parts as well. not sure though!
  
 +=== Blackbox ===
 +Thanks, but I'm still confused. Based on your explanation, "good" states seems like to have only diagonal terms in the matrix. I thought that it has some relation with a balance of fine structure and zeeman effect.
  
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classes/2009/fall/phys4101.001/q_a_1214.1260943422.txt.gz · Last modified: 2009/12/16 00:03 by ely

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