The rigorous relations between the propagators of transient Schr¨odinger equations and stationary Green functions are established.Based on the generalized Fourier transform,non-singular transparent boundary condi...The rigorous relations between the propagators of transient Schr¨odinger 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 Schr¨odinger 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.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12171035,11671038).
文摘The rigorous relations between the propagators of transient Schr¨odinger 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 Schr¨odinger 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.
