(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A wavefunction of angular momentum states is given:

[tex]\psi = \frac{1}{\sqrt{7}}|1,-1\rangle + \frac{\sqrt{35}}{7}|1,0\rangle+\sqrt{\frac{1}{7}}|1,1\rangle[/tex]

Calculate [tex]\langle \psi| L_{\pm} |\psi \rangle[/tex] and [tex]\langle 1,1|L_+^2|\psi\rangle[/tex]

3. Attempt at a solution.

If the wavefunction and angular momentum operators were given in matrix form, I would be able to solve this, since I know how it all works in the matrix representation.

But I am confused about what to do with dirac notation? I'm not really sure, should I convert the operators and kets into a matrix form... (I'm not sure how to do this either??). Griffiths, the text I'm using, didn't really go much into expectation values for angular momentum, or the matrix representation, so I would really appreciate some tips on where to go to from here. Thanks!

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# Expectation value for angular momentum

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