QMBlender: Particle-based visualization of 3D quantum wave function dynamics

Abstract

Simulated three-dimensional quantum wave functions (or probability density distributions, in general), Ψ(x, t), are often represented graphically as smooth isocontours or with 2-dimensional cross-sectional plots. As such, neither the full wave dynamics nor the true stochastic interpretation are captured adequately in a single representation. Moreover, the dynamics are often provided as videos, so that posterior interaction with the solution by other researchers is not possible. Here, we describe a software tool, called QMBlender, that produces 3D models of Ψ(x, t) at each time as a collection of Monte Carlo sampled coordinates represented by graphics primitives, or particles. QMBlender is a plugin to the popular open source Blender editor, which takes advantage of all its 3D editing, I/O, materials/lighting, and rendering capabilities. The resulting 3D models allow for posterior web-based interactive exploration, which we describe and argue could be a new paradigm for communicating and sharing results of numerical simulations. QMBlender can also be executed in a batch pipeline for producing 3D models, without the need for using the Blender GUI. We also implemented the particle sampling and visualization method using the VTK library for a side-by-side comparison with QMBlender. Here algorithms, implementation details, comparison with other similar systems, and examples from simulation of the Schrodinger equation are provided to show the utility of this software tool.