论文标题
一项关于物质波通过缝隙散射的研究
A Study on the Scattering of Matter Waves through Slits
论文作者
论文摘要
使用Feynman路径的整体形式主义探索了物质波通过缝隙的散射。我们明确绘制接近零的概率密度，以分析缝隙附近的行为。这样一来，引人入胜的模式就出现了，最著名的是在双缝隙的情况下，辫子状结构的复杂性会增加，随着缝隙的增加而增加。此外，该图显示了过渡区域的存在，其中接近零概率点的分布从编织到边缘样结构变化，已通过明确表达波函数作为超几何函数来分析。在考虑连续性方程式及其对概率密度为零的区域的后果时，对这些模式进行了分析。结果，我们发现可以控制大小的区域中的准陷阱，并使物质波的波长小得多。
Scattering of matter waves through slits has been explored using the Feynman Path Integral formalism. We explicitly plot the near-zero probability densities to analyse the behaviour near the slit. Upon doing so, intriguing patterns emerge, most notably the braid-like structure in the case of double slits, whose complexity increases as one increases the number of slits. Furthermore, the plot shows the existence of a transition region, where the distribution of near-zero probability points changes from the braided to the fringe-like structure, which has been analysed by explicitly expressing the wavefunction as a hypergeometric function. These patterns are analysed while considering the continuity equation and its consequences for the regions with zero probability density. As a result, we find quasi-traps in the region whose size can be controlled and made much smaller than the wavelength of matter waves.
