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Quantum Mechanics of Multi-Prong Potentials

机译:多叉势的量子力学

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摘要

We describe the bound state and scattering properties of a quantum mechanical particle in a scalar N-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy levels for the special case of N identical prongs exhibit an alternating pattern of non-degeneracy and (N−1) fold degeneracy. It is shown that the techniques of supersymmetric quantum mechanics can be used to generate new solutions. Solutions for prongs of arbitrary lengths are developed. Discussions of tunneling in N-well potentials and of scattering for piecewise constant potentials are given. Since our treatment is for general values of N, the results can be studied in the large N limit. A somewhat surprising result is that a free particle incident on an N-prong vertex undergoes continuously increased backscattering as the number of prongs is increased.
机译:我们描述了标量N-prong势中量子力学粒子的束缚态和散射特性。这样的研究特别有趣,因为这些情况介于一维和二维之间。 N个相同叉的特殊情况下的能级表现出非简并和(N-1)倍简并的交替模式。结果表明,超对称量子力学技术可以用来产生新的解。开发了任意长度的插脚的解决方案。讨论了N阱电位中的隧穿和分段恒定电位的散射。由于我们的处理是针对N的一般值,因此可以在较大的N限制下研究结果。有点令人惊讶的结果是,随着叉头数量的增加,入射在N叉形顶点上的自由粒子会不断增加反向散射。

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