Update on Mathematics and Physics HW set

The Pauli matrix for 3.b) should read like this

S_z   =   \frac{\hbar}{2}  \begin{pmatrix}   1 & 0 \\  0 & -1  \end{pmatrix}\,;
That is, there is a minus sign in the lower right corner of the matrix.
Otherwise, the eigenvalues become trivial for an identity.

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