Bra-kets and operator formalism in QM - Expectation values of momentum

Dixanadu
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Homework Statement


sup guys!

I think I've solved this set of problems, but I was just wondering if I've done it right - I have no way to tell. I'll put all the questions and answers here - plus the stuff I used. So could you please tell me if there's any mistakes?
Here it is - using Word as always!
http://imageshack.com/a/img4/750/6i29.png


Homework Equations



http://imageshack.com/a/img266/4082/58m3.jpg

BTW - I just realized I put in the transpose symbol instead of the dagger - i meant the dagger for the raising operator!

The Attempt at a Solution


http://imageshack.com/a/img546/7347/1oty.jpg
 
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My solutions are here, have a look..
 

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If you are careful with the manipulations of the operators, it's an easy problem.
 

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