Speaker
Description
In quantum mechanics, the wave function describes the state of a physical system. In the non-relativistic case, the time evolution of the wave function is described by the time-dependent Schrödinger equation. In 1982, D Kosloff and R Kosloff proposed a method [1] to solve the time-dependent Schrödinger equation efficiently using Fourier transformation. In 2020, Géza István Márk published a paper [2] describing a computer program for the interactive solution of the time-dependent and stationary two-dimensional (2D) Schrödinger equation. Some details of quantum phenomena are only observable by calculating with all three spatial dimensions. We found it worth stepping out from the two-dimensional plane and investigating these phenomena in three dimensions. We implemented the said method for the three-dimensional case to simulate the time evolution of the wave function. We used our implementation to simulate typical quantum phenomena using wave packet dynamics. First, we tried the method on analytically describable cases, such as the simulation of the double-slit experiment, and then we investigated the operation of flash memory. We used raytraced volumetric visualization to render the resulting probability density. In our work, we introduce the basics of wave packet dynamics in quantum mechanics. We describe the method in use in detail and showcase our simulation results.
For further information and animations, please visit
https://zoltansimon.info/src/content/research/wavepacketsim.html
References
[1] Kosloff, D., & Kosloff, R. (1983). A Fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics. Journal of Computational Physics, 52(1), 35–53. https://doi.org/https://doi.org/10.1016/0021-9991(83)90015-3
[2] Márk, G. I. (2020). Web-Schrödinger: Program for the interactive solution of the time dependent and stationary two-dimensional (2D) Schrödinger equation. https://doi.org/10.48550/arXiv.2004.10046
