Finding the expectation value of energy using wavefunc. and eigenstate

1. Oct 13, 2013

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. Oct 13, 2013

TSny

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. Oct 14, 2013

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. Oct 14, 2013