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 - <p style="text-align: justify;">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.</p>