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Finding the expectation value of energy using wavefunc. and eigenstate

  • Thread starter Dixanadu
  • Start date
  • #1
254
2

Homework Statement


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]


Homework Equations



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

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!
 
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Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,490
2,917
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.
 
  • #3
254
2
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...
 
  • #4
254
2
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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