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Finding the expectation value of energy using wavefunc. and eigenstate

  1. Oct 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey guys!

    So this is a bit of a long question, I've done most of it but I need a few tips to finish the last part, and I'm not sure if i've done the first one correctly. I'll be typing it up in Word cos Latex is long!

    http://imageshack.com/a/img5/8335/n7iw.jpg [Broken]


    2. Relevant equations

    http://imageshack.com/a/img820/2584/viiw.jpg [Broken]

    3. The attempt at a solution
    http://imageshack.com/a/img534/1410/lbv9.jpg [Broken]

    Please let me know if I've done part (a) right and a bit of a hint with part C. Thanks guys!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 13, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello.

    Your work looks pretty good. For part (a) I get a result that differs from yours by a factor of 2.

    For part (b), the high probability for ##P_1## should not be too surprising if you graph the state ##\Psi(x,0)## and compare it to the graph of ##\psi_1(x)##.

    For (c), there is an expression in the "stuff we need" that you can use.
     
  4. Oct 14, 2013 #3
    Okay, I dont know why your answer differs by a factor of 2 for part (a). Unless ive made a serious mistake I dont see how.

    Second, for part (c), I have no idea what to do. If I use the expression of <E> in terms of the sum of probabilites in the "stuff we need" section, I still have a factor of E_n on the RHS, dont know how to get rid of it...
     
  5. Oct 14, 2013 #4
    Oh dont worry about it TSny! I managed to figure it out. You were right, as always :D thanks for the help! I got the same answer for part (c) as you did for part (a).
     
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