Bhom's hydrodynamic formulation (or quantum fluid dynamics) is an attractive approach since, it connects classical and quantum mechanical theories of matter through Hamilton-Jacobi (HJ) theory, and quantum potential. Lopreore and Wyatt derived and implemented one-dimensional quantum trajectory method (QTM), a new wave-packet approach, for solving hydrodynamic equations of motion on serial computing environment. Brook et al. parallelized the QTM on shared memory computing environment using a partially implicit method, and conducted accuracy study of a free particle. These studies exhibited a strange behavior of the relative error for the probability density referred to as the transient effect. In the present work, numerical experiments of Brook et al. were repeated with a view to identify the physical origin of the transient effect and its resolution. The present work used the QTM implemented on a distributed memory computing environment using MPI. The simulation is guided by an explicit scheme.