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[QUE/QM-07011]

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A physical system has dynamical variables $X,Y,Z$ represented by the  $2\times2$ Pauli matrices $\sigma_x,\sigma_y,\sigma_z$.
Compute the average value of $\ell X + m Y + n Z $ in any one state in   which $a X + b Y + c Z $ has a definite value. Assume        $\ell^2 + m^2 +n^2=1$ and $a^2 + b^2 + c^2=1$.

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