Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive Grids

TL;DR

This paper discusses the development of computational methods using quantum trajectories and adaptive grids to solve hydrodynamical equations in quantum mechanics, enhancing simulation capabilities.

Contribution

It introduces new techniques for implementing quantum trajectories with adaptive grids and Gaussian fitting, improving computational efficiency in quantum hydrodynamics.

Findings

Effective trajectory-based computational methods developed

Gaussian cluster fitting enhances accuracy

Adaptive grids improve simulation efficiency

Abstract

Although the foundations of the hydrodynamical formulation of quantum mechanics were laid over 50 years ago, it has only been within the past few years that viable computational implementations have been developed. One approach to solving the hydrodynamic equations uses quantum trajectories as the computational tool. The trajectory equations of motion are described and methods for implementation are discussed, including fitting of the fields to gaussian clusters.