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arXiv 1504.07530quant-ph
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路径积分与双缝

Path integrals and the double slit

Eric Jones, Roger Bach, Herman Batelaan

摘要:

对双缝衍射现象的基本解释包括对从两条缝发出并干涉的波的描述。干涉最小值和最大值的位置由波的相位差确定。具有波长$λ$并传播距离$L$的光波累积相位$2πL{/}λ$。同样具有波长$λ$并且传播相同距离$L$的物质波累积相位$πL{/}λ$,其是与光学情况不同的两倍。然而,对于传播距离相差$ΔL$的干扰物质波,相位差$Δϕ$近似为$2πΔL{/}λ$,这与光学情况下计算的值相同。物质和光学情况之间的差异阻碍了基于物质-光学类比的双缝衍射的概念解释。在下面的文章中,我们提供了一个路径积分描述的物质波的概念解释的重点。通过一个思想实验说明了近似$Δϕ{\approx}2πΔL{/}λ$的有效范围。

英文摘要:

Basic explanations of the double slit diffraction phenomenon include a description of waves that emanate from two slits and interfere. The locations of the interference minima and maxima are determined by the phase difference of the waves. An optical wave, which has a wavelength $λ$ and propagates a distance $L$, accumulates a phase of $2πL{/}λ$. A matter wave, also having wavelength $λ$ and propagating the same distance $L$, accumulates a phase of $πL{/}λ$, which is a factor of two different from the optical case. Nevertheless, the phase difference, $Δϕ$, for interfering matter waves that propagate distances that differ by $ΔL$, is approximately $2πΔL{/}λ$, which is the same value computed in the optical case. The difference between the matter and optical case hinders conceptual explanations of diffraction from two slits based on the matter-optics analogy. In the following article we provide a path integral description for matter waves with a focus on conceptual explanation. A thought experiment is provided to illustrate the validity range of the approximation $Δϕ{\approx}2πΔL{/}λ$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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