The Schrodinger equation is a linear ODE for the time
evolution of a state vector in a Hilbert space. One may instead
consider this equation as giving the time evolution of a unitary
operator on that Hilbert space. We will give an explicit expression for
this ODE in the case that the unitary operator lies in a Lie group by
passing to the corresponding Lie algebra. The Lie group SU(2) will be
worked out in detail.