[QUE/QM-09009]

For a spin half particle in a uniform magnetic field \(\vec{B}\) the Hamiltonian is given by \[H=-\vec{\mu}\cdot\vec{B}\] where the magnetic moment is \(\vec{\mu} = \gamma \frac{e\hbar}{2mc}\vec{\sigma}\) and \(\vec{\sigma}\)    are Pauli spin matrices, \(\gamma\) is a constant. 

1. Find the magnetic moment operator in the Heisenberg picture.
2. Derive equation of motion for the spin \(\vec{S}\) and show that the spin precesses about the magnetic field.