This thesis is concerned with studying chemical dynamics using time-dependent quantum mechanics and in particular using the Fourier method. Various ways of implementing the Fourier method are described, both for calculations in one dimension and for those in many dimensions. The Fourier method is then used to simulate time-resolved femtosecond and picosecond pump-probe experiments, which investigate the B state of the sodium trimer. The simulation is divided into three stages: the initial wavefunction is generated by modelling the effect of the pump laser pulse on the ground state wavefunction of the X state of the sodium trimer; the wavepacket now on the B state is propagated in time; the observables are extracted from the time-dependent wavefunction. The calculations are carried out initially in two dimensions, corresponding to the bending and asymmetric stretch normal modes, and then in three dimensions, i.e. including the symmetric stretch normal mode. The simulation of the time-resolved experiments produced physically plausible results. The correspondence with the experimental results was only fair, but this could be mostly accounted for by the poor quality of the potential energy surfaces used. Thus, even the relatively simple model used to simulate the time-resolved experiments is useful to gain both a qualitative explanation of the results of these experiments and an insight into the dynamics of systems which are in non-stationary states
