实时波包散射问题
Scattering Problems via Real-time Wave Packet Scattering
摘要：
在本文中，我们使用一个简单的数值方法来解决散射模型在一维晶格的紧束缚能带结构的基础上。我们通过使用散射的波包方法来做到这一点，该方法比传统的平面波方法呈现出更直观的物理图像。此外，一般的矩阵对角化方法，是很容易获得的本科生在量子力学的第一门课程。首先简要回顾了连续极限中的波包输运，并与晶格中的波包输运进行了比较。通过对角化方法得到的数值结果，然后对分析结果进行基准。共振二聚体的情况下，在晶格中进行了研究，并确定了几个共振值的平均波包动量。通过研究晶格中的等效情况，比较了平面波入射到阶梯势和矩形势垒上的透射系数。最后，我们提出了几个简短的模拟散射过程，强调如何使用一个简单的方法来可视化一些显着的现象。
英文摘要：
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. Lastly, we present several short simulations of the scattering process which emphasize how a simple methodology can be used to visualize some remarkable phenomena.
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