Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 701-719.
Published online: 2023-08
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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} }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.