Sound Synthesis of a Gaussian Quantum Particle in an Infinite Square Well

Abstract

Abstract This article describes a synthesis technique based on the sonification of the dynamic behavior of a quantum particle enclosed in an infinite square well. More specifically, we sonify the momentum distribution of a one-dimensional Gaussian bouncing wave packet model. We have chosen this particular case because of its relative simplicity and interesting dynamic behavior, which makes it suitable for a novel sonification mapping that can be applied to standard synthesis techniques, resulting in the generation of appealing sounds. In addition, this sonification might provide useful insight into the behavior of the quantum particle. In particular, this model exhibits quantum revivals, minimizes uncertainty, and exhibits similarities to the case of a classical bouncing ball. The proposed model has been implemented in real time in both the Max/MSP and the Pure Data environments. The algorithm is based on concepts of additive synthesis where each oscillator describes the eigenfunctions that characterize the state evolution of the wave packet. We also provide an analysis of the sounds produced by the model from both a physical and a perceptual point of view.