where Ĥ is the Hamiltonian matrix (which implicitly depends on the density matrix), S -1 is the inverse of the overlap matrix, and h is Planck's constant. Furthermore, because the quantum system is directly propagated in the time domain, one can choose E 0 (t) to have any time-dependent form. For example, if E 0 (t) is chosen to have the form of a Dirac delta function given by