I am wondering if it is possible to solve the following system of ODEs. Would it be possible to use matrix exponential in the way it was used Here?
$$\left[ {\begin{array}{cc} a_{1}(t) \\ a_{2}(t)\\ \end{array} } \right]^{'} = \left[ {\begin{array}{cc} 0 & \frac{H_{12}}{i\hbar}cos(\frac{2\pi t}{T}) \\ \frac{H_{12}}{i\hbar}cos(\frac{2\pi t}{T}) & \frac{\Delta E}{i \hbar} \\ \end{array} } \right] \left[ {\begin{array}{cc} a_{1}(t) \\ a_{2}(t)\\ \end{array} } \right]$$