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Bohmian trajectories of the time-oscillating Schrödinger equations
Dandan Li1, Jinqiao Duan2, Li Lin1
1School of Mathematics and Statistics and Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China.
Abstract:
Bohmian mechanics is a non-relativistic quantum theory based on a particle approach. In this paper, we study the Schrödinger equation with a rapidly oscillating potential and the associated Bohmian trajectory. We prove that the corresponding Bohmian trajectory converges locally in a measure, and the limit coincides with the Bohmian trajectory for the effective Schrödinger equation on a finite time interval. This is beneficial for efficient simulation of the Bohmian trajectories in oscillating potential fields.
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