Transient Effect of a Free Particle Wave Packet in the Hydrodynamic Formulation of the Time-dependent Schrödinger Equation

Vadapalli, R. K., Weatherford, C. A., Banicescu, I., Carino, R.L., & Zhu, J. (2003). Transient Effect of a Free Particle Wave Packet in the Hydrodynamic Formulation of the Time-dependent Schrödinger Equation. International Journal of Quantum Chemistry. Wiley Periodicals, Inc. 94(1), 1-8.

Abstract

This article scrutinizes anomalies in accuracy studies by Brook et al. [Int J Quantum Chem 2001, 85, 263-271] for a moving free particle. These studies were carried out in the framework of the quantum trajectory method developed from Bohm\'s hydrodynamic formalism. These accuracy studies exhibited a strange behavior of the relative error in the probability density that apparently contradicts the quantum fluid dynamic formalism. It is found that improper initialization of the pseudoparticle velocities is responsible for the observed anomalies. This article presents a method for appropriate initialization of the pseudoparticle velocities. It also evaluates the accuracy of this method by reinvestigating accuracy studies by Brook et al. for a moving free particle.