应用于量子含时波包方法的高精度透明边界条件

本文提出了一种适用于量子含时波包方法的透明边界条件. 该量子含时波包方法结合分离变量表象方法使用的时候，本质上是具有谱收敛性质的. 相对于以往的复数吸收势，该透明边界条件的突出优点是其对于波函数的能谱分布并不敏感. 采用具有共振态的一维势垒散射模型，本文对该方法的特点做了阐述.

High-Accurate Transparent Boundary Conditions for Time-Dependent Quantum Wave Packet Method

Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region. Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range, particularly involving ultra-low energy. In this work, a new transparent boundary condition (TBC) is proposed for the time-dependent wave packet method. It in principle is of spectral accuracy when typical discrete variable representations are applied. The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function, in contrast with the complex absorbing potential. Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well, which supports resonances states.