标题： 超周期势 显示英文标题

标题： Super Periodic Potential

摘要： 本文中我们引入了一维任意阶超周期势（SPP）的概念，即 $n$, $n \in I^{+}$。给出了二阶超周期势（$n$）中波传播的一般理论，并通过传递矩阵方法以封闭解析形式推导出反射系数和透射系数。我们将超周期矩形势垒和超周期 δ 势作为 SPP 的特例，研究了它们的散射特性。发现对称自相似性是超周期性的特殊情况。因此，通过将对称分形势识别为 SPP 的特殊情况，可以得到粒子从这种分形势中隧穿的概率幅。利用 SPP 的形式体系，我们得到了一般康托势和 Smith-Volterra-Cantor 势的粒子隧穿概率幅的闭式表达式。 显示英文摘要

摘要： In this paper we introduce the concept of super periodic potential (SPP) of arbitrary order $n$, $n \in I^{+}$, in one dimension. General theory of wave propagation through SPP of order $n$ is presented and the reflection and transmission coefficients are derived in their closed analytical form by transfer matrix formulation. We present scattering features of super periodic rectangular potential and super periodic delta potential as special cases of SPP. It is found that the symmetric self-similarity is the special case of super periodicity. Thus by identifying a symmetric fractal potential as special cases of SPP, one can obtain the tunnelling amplitude for a particle from such fractal potential. By using the formalism of SPP we obtain the close form expression of tunnelling amplitude of a particle for general Cantor and Smith-Volterra-Cantor potentials.