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I believe this to be a rather simple problem but I am not quite sure if my thinking is correct.

We have a particle in a j=1 state of angular momentum J. I am first asked to find some eigenvectors of the matrix J(y):

[tex]J_{y}=\frac{\hbar}{\sqrt{2}i}\begin{pmatrix} 0 & -1 & 0\\ 1 & 0 & -1\\ 0 & -1 & 0 \end{pmatrix}[/tex]

Is this correct?

I got the eigenvalues of this matrix to be i√2, -i√2 and 0 which I believe correspond, respectively to,

[tex]\hbar, -\hbar, 0[/tex]

Though my main question (provided the above is correct) is that we are told the system is in a state of the J(y) corresponding to the positive non-zero eigenvector, we are then asked to find the probability of finding each value :

[tex]\hbar, -\hbar, 0[/tex]

of the J(z) angular momentum.

Surely this is just given by the normalized coefficients of the eigenvectors of J(z) and the fact it is in a state of J(y) is not relevant?

I can post the eigenvectors I attained for the J(y) matrix if required.

Thanks,

SK

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# Successive Measurements of angular momentum

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