A quantum mechanical system is described by vectors $\psi=\left(\begin{array}{l}a \\ b\end{array}\right)$. The energy eigenvectors are

$$\psi_{0}=\left(\begin{array}{c} \cos \theta \\ \sin \theta \end{array}\right), \quad \psi_{1}=\left(\begin{array}{c} -\sin \theta \\ \cos \theta \end{array}\right)$$

with energies $E_{0}, E_{1}$ respectively. The system is in the state $\left(\begin{array}{l}1 \\ 0\end{array}\right)$ at time $t=0$. What is the probability of finding it in the state $\left(\begin{array}{l}0 \\ 1\end{array}\right)$ at a later time $t ?$