[QUE/SM-03015] SM-PROBLEM

Find the density matrix of an ensemble of spin half prepared with 60 percent have $\sigma_z\,=\,+1$ and 40 percent have $\sigma_x\,=\,1$. Use the eigenstates of $\sigma_z$ as the basis. If the system is subjected to a magnetic field ( from time $t\,=\,0$) find the density matrix as a function of time. Assume the Hamiltonian is given by $H\,=-\,\mu B_0\sigma_z $ where $\mu\,B_0$ are a constants.

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