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## GR0877 Problem 64

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (D) Eigenvalues of $L^2$ are $\hbar^2 l(l+1)$, eigenvalues of $L_z$ are $m \hbar$. Thus, $(\sqrt{2} \hbar)^2 = \hbar^2 l(l+1)$, from which $l = 1$. For a given $l$, there are $2l+1$ different values of $m$: $m = -l,-l+1,\dots, l-1, l$. In our case, $m = -1, 0, 1$ and, therefore, the possible values of $L_z$ are $-\hbar, 0, \hbar$.

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