The problem involves measurement in a quantum system with angular momentum. There are two parts I am struggling with. Apologies for the images, I tried to put it all in latex but failed!(adsbygoogle = window.adsbygoogle || []).push({});

Part 1:

[PLAIN]http://i2.sqi.sh/s_1/1xo/part1.jpg [Broken]

I have found a long derivation in a book involving a function Y_{lm}, but I am sure I must be missing a simple trick to derive the eigenvalues simply from this data given? I have found that the eigenvalue should be mh, but I am stumped as to how I can find this from L^{2}. Any hints are welcome.

Part 2:

[PLAIN]http://i2.sqi.sh/s_1/1xp/part2.jpg [Broken]

I have no problem with the first part of this question, finding the eigenvalues with respect to L^{2}and L_{z}, but the second part has me stumped.

My eigenvalues are as follows, found using a form of L^{2}and L_{z}given previously in the question.

Firstly for L^{2}

[tex]2\,{h}^{2}, 2\,{h}^{2}+{\frac {{h}^{2}}{{\sin}^{2}\theta}}, 2\,{h}^{2}-{\frac {{h}^{2}}{{\sin}^{2}\theta}[/tex]

And for L_{z}

[tex]0, -h, h[/tex]

My problem is, I'm not sure what a simultaneous measurement is? I can see that the answers given are simply the eigenvalues for L_{z}, and one of the eigenvalues for L^{2}, but I'm not quite sure how they are connected?

I am also not sure about the final part of this question. Should I try to write [tex]\Psi[/tex] as a linear combination of u1, u2 and u3?

Thanks in advance for any help, I think my main problem is interpreting what I should be finding, I don't think the maths will be that difficult.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Quantum Mechanics, Angular Momentum Measurement Problem

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