TY - JOUR T1 - Green Function Method for Quantum Transport Based on the Generalized Fourier Transform AU - Jiang , Haiyan AU - Gao , Xingming AU - Hu , Yueguang AU - Lu , Tiao JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 701 EP - 719 PY - 2023 DA - 2023/08 SN - 16 DO - http://doi.org/ 10.4208/nmtma.OA-2022-0164 UR - https://global-sci.org/intro/article_detail/nmtma/21963.html KW - Schrödinger equation, Green function, generalized Fourier transform, transparent boundary condition. AB -

The rigorous relations between the propagators of transient Schrödinger equations and stationary Green functions are established. Based on the generalized Fourier transform, non-singular transparent boundary condition for transient problem is proposed in a representation of Green functions. The unified framework of Green function method is presented for converting an open boundary problem into a bounded boundary problem. Numerical scheme for time-dependent Schrödinger equation with non-singular transparent boundary condition is designed to simulate the propagations of a free Gaussian wave packet and the resonant tunnelling through double barriers. Numerical results validate the effectiveness of non-singular transparent boundary condition.