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Hi people,

I'm struggling with my quantum mechanics homework - I've included links to photographs of my attempts at solutions, but i know they are wrong because I am given what the answers are supposed to be. Can somebody help me spot where I am going wrong? I dont have a keyboard key for psi(x) so i'll use Y(x) for wavefunctions. Here is the question:

My particle, described by the wavefunction Y(x) = Ax(L-x) is confined to a region 0<x<L.

A is a constant.

a) Normalize the wavefunction to unity.

b) Compute the average value of position <x> , <x^2> , <p> and <p^2>.

Here is my solution to part a).

Have i done what is being asked of me, ie. square the wavefunction, and set the integral of that, within the limits of x, equal to 1??

http://i52.photobucket.com/albums/g33/long_john_cider/normalization.jpg

Here are my solutions to part B.

The thing about these ones is, i dont think there is a problem with my actual calculations since I have done them a few times and got the same result. I think its with the initial equations for <x>, <x^2>, <p> and <p^2> that I start out with.

<x>: http://i52.photobucket.com/albums/g33/long_john_cider/xavexpv.jpg

<x^2>: http://i52.photobucket.com/albums/g33/long_john_cider/x2avexpv.jpg

I am supposed to use these answers to get this result, but my answer is nowhere near:

Δx = sqrt(<x^2> - <x>^2) = L / sqrt(28)

<p>: http://i52.photobucket.com/albums/g33/long_john_cider/p2avexpv.jpg

<p^2>: http://i52.photobucket.com/albums/g33/long_john_cider/p2avexpv.jpg

I am supposed to use these answers to get this result, but again my answer is nowhere near:

Δp = sqrt(<p^2> - <p>^2) = H(sqrt(10) / L

where H = h/2pi , h bar in other words.

Can anybody spot what I am doing wrong? I greatly appreciate any help because I have followed my notes perfectly but I am still getting the wrong answers.

Thanks.

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# Homework Help: Quantum homework - Average Expectation Values?

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