Finite Element Approach for Simulating Quantum Electron Dynamics in a Magnetic Field

Abstract

A fast and stable numerical method is formulated to compute the time evolution of a wave function in a magnetic field by solving the time-dependent Schrödinger equation. This computational method is based on the finite element method in real space to improved accuracy without any increase of computational cost. This method is also based on Suzuki's exponential product theory to afford an efficient way to manage the TD-Schr{ö}dinger equation with a vector potential. Applying this method to some simple electron dynamics, we have confirmed its efficiency and accuracy.