Parallel computers are finding major applications in almost all scientific and engineering disciplines. An interesting area that has received attention is quantum scattering. Algorithms for studying quantum scattering are computation intensive and hence suitable for parallel machines. The state-of-the-art methods developed for uniprocessors require the computation of two Fast Fourier Transforms (FFTs) at each time step. However, the communication overhead in implementing FFTs make them an expensive operation on distributed memory parallel machines;The focus of this dissertation is the development of efficient parallel methods for studying the phenomenon of time-dependent quantum-wave scattering. The methods described belong to the class of integral equation methods, which involve the application of a repeated sequence of very short time step propagations. Free propagation of a wavepacket is most easily handled in the so-called momentum representation whereas the effect of the potential is most easily obtained in the coordinate representation. The two representations are Fourier Transforms of each other. The algorithm presented eliminates the computation of FFTs by performing the propagation totally within the coordinate representation. The communication required is only with the nearest neighbors and is load balanced, thus making the algorithm suitable for distributed memory parallel machines. Implementation results on the nCUBE hypercube and comparison with standard FFT methods are also presented.