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classes:2009:fall:phys4101.001:q_a_1130 [2009/12/01 20:11] – x500_hakim011classes:2009:fall:phys4101.001:q_a_1130 [2009/12/16 00:44] (current) – czhang
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 ====Dark Helmet 11/28 === ====Dark Helmet 11/28 ===
 Can we perhaps get another count of Pre-lecture Q/A points? Can we perhaps get another count of Pre-lecture Q/A points?
 +
 +=== The Doctor ===
 +Perhaps...
 +
 ====Schrodinger's Dog 11/29==== ====Schrodinger's Dog 11/29====
 On page 244, Griffiths mentions that he multiplies the degeneracy dk by 2 because of the spin. When we are talking about photons, I usually hear that this factor of 2 comes from the polarization of light, and the fact that it photons can only travel transversely. What is the story? Did we first think it was 2 when we working semi-classical(i.e. before modern QM) and then discovered spin, and accounted this factor of 2 because of spin in modern QM? On page 244, Griffiths mentions that he multiplies the degeneracy dk by 2 because of the spin. When we are talking about photons, I usually hear that this factor of 2 comes from the polarization of light, and the fact that it photons can only travel transversely. What is the story? Did we first think it was 2 when we working semi-classical(i.e. before modern QM) and then discovered spin, and accounted this factor of 2 because of spin in modern QM?
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 ===Schrodinger's Dog 11/30=== ===Schrodinger's Dog 11/30===
 It takes into account the nucleus, when looking at the atom, and taking into account the nucleus allows you to see the fine-structure splitting, which is discussed in chapter 6. They simply replace m with mu, and you get a split in the regular energy levels you see.  It takes into account the nucleus, when looking at the atom, and taking into account the nucleus allows you to see the fine-structure splitting, which is discussed in chapter 6. They simply replace m with mu, and you get a split in the regular energy levels you see. 
 +
 +=== Can 12/16 ===
 +It depends which particle you treated as stationary. Take the hydrogen atom as an example, for simplicity we treated the nucleus as stationary only the electron is rotating about the nucleus, which is not necessarily true.  remember the reduced mass equation is <math>m_r=\frac{m_e*m_p}{m_e+m_p}</math>, mass of electron is negligible compare to proton, thus normally the reduced mass of electron is just m_e, but if we treated the electron stationary and nucleus evolving about electron, things would be different.
 + 
  
 ==== Blackbox 11/30 10:50am ==== ==== Blackbox 11/30 10:50am ====
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 I know the spin part of the wave function is sort of an "addition" to the x-dependent part of the wave function, it just wasn't included in Chapter 2 because we weren't considering spin at that point. I know the spin part of the wave function is sort of an "addition" to the x-dependent part of the wave function, it just wasn't included in Chapter 2 because we weren't considering spin at that point.
  
-===Andromeda 12/01 8:05===+===Andromeda 12/01 8:05pm===
 I think the time dependent wave function for two or more electrons is a combination of their space eigenfunction and spin eigenfunction. Both space eigenfunction and spin eigenfunction will have a time dependent part and can be one of the symmetric states or antisymmetric states. we just have to make the total wave function be antisymmetric for antisymmetric particles like electron, proton... and symmetric for symmetric particles like photons...  I think the time dependent wave function for two or more electrons is a combination of their space eigenfunction and spin eigenfunction. Both space eigenfunction and spin eigenfunction will have a time dependent part and can be one of the symmetric states or antisymmetric states. we just have to make the total wave function be antisymmetric for antisymmetric particles like electron, proton... and symmetric for symmetric particles like photons... 
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 ==== Hardy 12/01 0:30 am==== ==== Hardy 12/01 0:30 am====
  
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 I thought I could answer this, but I cannot. I scoured the book, and everything just comes down to the statements on page 106 that a measurement of an observable must yield one of the eigenvalues of that observable. This statement comes with no explanation, but Griffiths specifically states that this is unlike anything in classical physics. I guess it's just one of those things in QM that you have to accept. I thought I could answer this, but I cannot. I scoured the book, and everything just comes down to the statements on page 106 that a measurement of an observable must yield one of the eigenvalues of that observable. This statement comes with no explanation, but Griffiths specifically states that this is unlike anything in classical physics. I guess it's just one of those things in QM that you have to accept.
 +
 +=== Yuichi ===
 +I guess you can say that this is a fundamental postulate for QM.  When a particle is trapped in an infinite square well, momentum (as well as the energy) can take only certain values, which is the eigenvalues of the momentum operator for the particle.  i.e. <math>p=\pm\frac{n\pi}{L}\hbar</math>.  The spin measurements that Hardy is talking about is no different from this case.  Or doesn't this analogy make any sense?
 +
 +====Andromeda 12/01 8:25 PM ====
 +How is <math/> p^2=1</math>??? i dont understand what he means by that. and how is its eigenvalues +/-1?
 +
 +=== The Doctor 12/02 1:45 AM ===
 +Where do you see this?
 +===Andromeda 12/2 7:32 Am===
 +Oh sorry, page 205-the exchange operator
 +===Jake22 12/2 7:42 pm===
 +Consider how operators can be treated as matrices and multiplied. When you multiply once by P, you interchange the two particles. If you multiply this product by P (obtaining <math/> p^2 f</math>), you interchange them again, which brings you to the same result that multiplying by 1 would have. For the eigenvalues, consider the matrix that transforms a vector (a,b) to (b,a). It is easy to see that this matrix has eigenvalues of +/-1.
  
 ====Pluto 4ever 12/01 4:19PM==== ====Pluto 4ever 12/01 4:19PM====
classes/2009/fall/phys4101.001/q_a_1130.1259719871.txt.gz · Last modified: 2009/12/01 20:11 by x500_hakim011

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