论文标题
转移矩阵的远程电势
Transfer matrix for long-range potentials
论文作者
论文摘要
我们将电势散射的传输矩阵的概念扩展到大型的远程电位$ V（x）$并得出其基本属性。我们概述了这类电位的时间无关散射理论的动态表述，在该理论中，我们将其传递矩阵与某些有效的非自动两级量子系统的$ s $ -matrix确定。对于$ | x | $的足够大的值，我们将$ v（x）$表示为短期潜力的总和和完全可解决的远距离电位。使用此结果以及传输矩阵的组成属性，我们概述了一个近似方案，用于解决$ v（x）$的散射问题。为了证明该方案的有效性，我们构建了一个准确的可解决的远距离电位，并将其反射和传输系数的确切值与使用近似方案获得的那些相比。
We extend the notion of the transfer matrix of potential scattering to a large class of long-range potentials $v(x)$ and derive its basic properties. We outline a dynamical formulation of the time-independent scattering theory for this class of potentials where we identify their transfer matrix with the $S$-matrix of a certain effective non-unitary two-level quantum system. For sufficiently large values of $|x|$, we express $v(x)$ as the sum of a short-range potential and an exactly solvable long-range potential. Using this result and the composition property of the transfer matrix, we outline an approximation scheme for solving the scattering problem for $v(x)$. To demonstrate the effectiveness of this scheme, we construct an exactly solvable long-range potential and compare the exact values of its reflection and transmission coefficients with those we obtain using our approximation scheme.
