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--- classes:2009:fall:phys4101.001:q_a_0921 [2009/09/21 19:39] – kuehler
+++ classes:2009:fall:phys4101.001:q_a_0921 [2009/09/26 23:42] (current) – yk
@@ Line 26: / Line 26: @@
 ====Hydra 14:30 9/20====
 How does this evenly-spaced ladder model agree with the non-evenly-spaced levels we see in, say, hydrogen?
-==Schrodinger's Dog==
+===Schrodinger's Dog 17:55 9/20===
 Where does it say that the SHO potential uses a evenly-spaced ladder model? And for hydrogen, Griffths didn't use the the ladder operators, he used spherical coordinates and some techniques in solving coupled differential equation. This may be cause they are "non-evenly-spaced levels". If there is a book on using ladder method use on the columb potential with hydrogen I ll check it out.
 ====vinc0053 9/20 20:08====
 How does Griffiths arrive at equations 2.65 (pg 48)?  I have looked over 2.57, 2.61, and 2.65 and cannot find the same conclusion.  Is he merely glossing over some aspects (as he often does) to cut to a nice proportionality?  I'm lost, and he uses 2.65 to simplify example 2.5.
@@ Line 45: / Line 46: @@
 ====chap0326 9/20 21:08====
 Does anyone know what the formula would be for finding the expectation value of the momentum squared?
-===Andromeda===
+===Andromeda 22:13 9/20===
 formula 1.36 in the book is the general function for finding an expectation value; so if you square the momentum operator and insert it in place of Q(x,p) in 1.36 you should have a formula for expectation value of momentum squared.
+===Green Suit 9/21 20:45===
+ Prof. Yuichi started this in class leaving us with: <math> <p^2>=\frac{-mh\omega}{2}\int\Psi_n^\ast [a_-^2 - (a_-a_+) - (a_+a_-)a_+^2] \Psi_n dx</math>. We also assertained that <math>a_-^2</math> and <math>a_+^2</math> both go to zero. From 2.65, <math> -(a_-a_+)=-(n+1)</math> and <math> -(a_+a_-)=-n</math>. These two are constants and get pulled out which now gives us: <math>-(2n+1)\frac{-mh\omega}{2}\int\Psi_n^\ast \Psi_n dx</math>. The two negatives cancle and solves the issue of negative momentum that Prof. Yuichi identified earlier.
+===== time to move on =====
-==== Mercury 9/21 15:00 ====
+It's time to move on to the next Q_A: [[Q_A_0923]]
-I know we kind of touched on this class, but I was confused about where the <math>\sqrt{1/2}</math> came from in the expression for a+ and a-?
-===Dagny 9/21 17:10===
-In discussion 2 solutions, shouldn't the coefficients in the time-dependent solutions, to the example problem, be 1/sqrt(2)? I am confused as to why they are 1/sqrt(a).
-===Pluto 4ever 9/21 19:35===
-What I understand is that from eq. 2.46 <math>a_-</math> and <math>a_+</math> are just the operators of the hamiltonian <math>H=1/2m[p^2+(m\omega\x)^2]</math>.

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