In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more intuitive physical picture than the traditional plane wave approach. Moreover, a general matrix diagonalization method that is easily accessible to undergraduate students taking a first course in quantum mechanics is used. Beginning with a brief review of wave packet transport in the continuum limit, comparisons are made with its counterpart in a lattice. The numerical results obtained through the diagonalization method are then benchmarked against analytic results. The case of a resonant dimer is investigated in the lattice, and several resonant values of the mean wave packet momentum are identified. The transmission coefficients obtained for a plane wave incident on a step potential and rectangular barrier are compared by investigating an equivalent scenario in a lattice. Finally, we present several short simulations of the scattering process, which emphasize how a simple methodology can be used to visualize some remarkable phenomena.

中文翻译：

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基于实时波包散射的散射问题

在本文中，我们使用一种简单的数值方法来求解基于紧束缚带结构的一维晶格中的散射模型。我们通过使用波包方法进行散射来实现这一点，它提供了比传统平面波方法更直观的物理图片。此外，还使用了一种通用矩阵对角化方法，该方法对于参加量子力学第一门课程的本科生来说很容易获得。首先简要回顾连续体极限中的波包传输，然后与格子中的对应物进行比较。然后将通过对角化方法获得的数值结果与分析结果进行对比。在晶格中研究了共振二聚体的情况，并确定了平均波包动量的几个共振值。通过研究晶格中的等效场景，比较了入射在阶跃电位和矩形势垒上的平面波的透射系数。最后，我们展示了散射过程的几个简短模拟，它们强调了如何使用简单的方法来可视化一些显着的现象。