In this study a multiprocessor C++ message passing interface implementation of a new bit-reversal algorithm to numerically solve the time dependent Schrodinger equation using a spectral method based on Fourier transform was presented. The major issues of parallel computer performance were discussed in terms of efficiency; speed up, cost and fraction of the execution time that could be parallelized. The scalable performance to a very high number of processors was addressed as well as compared with ideal values of Amdahl’s Law when presenting the parallel performance of the new developed algorithms. The results showed that message passing interface was an optimal method of implementing a parallelized bit-reversal algorithm.