Theses and Dissertations

Issuing Body

Mississippi State University


Skjellum, Anthony

Committee Member

Huddleston, David H.

Committee Member

Oppenheimer, Seth F.

Date of Degree


Document Type

Graduate Thesis - Open Access


Computational Engineering (Program)

Degree Name

Master of Science


College of Engineering


Computational Engineering Program


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.