@Article{NMTMA-16-701, author = {Jiang , HaiyanGao , XingmingHu , Yueguang and Lu , Tiao}, title = {Green Function Method for Quantum Transport Based on the Generalized Fourier Transform}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {3}, pages = {701--719}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/ 10.4208/nmtma.OA-2022-0164}, url = {http://global-sci.org/intro/article_detail/nmtma/21963.html} }