Bohmian Trajectories of the Time-oscillating Schrödinger Equations
Dandan Li, Jinqiao Duan, Li Lin, Ao Zhang
Abstract
Bohmian mechanics is a non-relativistic quantum theory based on a particle approach. In this paper we study the Schrödinger equation with rapidly oscillating potential and the associated Bohmian trajectory. We prove that the corresponding Bohmian trajectory converges locally in measure, and the limit coincides with the Bohmian trajectory for the effective Schrödinger equation on a finite time interval. This is beneficial for the efficient simulation of the Bohmian trajectories in oscillating potential fields.