Suppose that the system starts in one of the basis states at t = 0 {\displaystyle t=0} , say | 1 ⟩ {\displaystyle |1\rangle } so that c 0 = ( 1 0 ) {\displaystyle \mathbf {c} _{0}={\begin{pmatrix}1\\0\end{pmatrix}}} , and we are interested in the probability of occupation of each of the basis states as a function of time when H {\displaystyle \mathbf {H} } is the time-independent Hamiltonian.