论文标题
Feynman在波光学元件中应用并用于计算量子概率电流
Feynman's Sum-over-Paths method applied in wave optics and for calculating the quantum probability current
论文作者
论文摘要
基于理查德·费曼（Richard Feynman）的总计方法，得出了一种计算波相量向量的集成方法。可以从此类相向量计算出各种缝隙掩模的衍射和干扰模式。结果与使用更复杂的菲涅尔积分计算的结果匹配。 Babinet首次提出了Babinet的阶段原则。例如，还可以通过从较大狭缝的较小缝隙中减去较小缝的相量来计算双缝的衍射图。当将障碍物放置在双缝后面时，还可以通过使用衍射计算工具来证明此方法。相位向量积分的方法扩展以计算量子概率电流。基于汉密尔顿 - 雅各布 - 和固定的schrödinger-方程，计算了量子概率电流，并显示了其连续性。概率电流速度的时间依赖性微分方程是数值求解的。对于大量集成，统计表明，每个区域的通量分布与概率密度曲线一致。还为横穿不对称双缝隙的光子模拟了量子概率电流，并讨论了特殊结果。
Based on the Sum-over-Paths approach of Richard Feynman, an integration method for calculating wave phase vectors is derived. The diffraction and interference patterns of various slit masks can be calculated from such phase vectors. The results obtained match with those computed using the more complex Fresnel integrals. Babinet's principle for phases is presented for the first time. As an example, the diffraction pattern of a double slit can also be calculated by subtracting the phase vectors of a smaller slit from those of a larger one. This method is also demonstrated by using a diffraction calculation tool when an obstacle is positioned behind a double slit. The approach of phase vector integration is expanded to calculate the quantum probability current. Based on the Hamilton-Jacobi- and the stationary Schrödinger- equation, the quantum probability current is calculated and its continuity is shown. The time-dependent differential equation of the probabilty current velocity is numerically solved. For a large number of integrations it is statistically shown that the distribution of the flux per area is consistent with the probability density profile. The quantum probability current is also simulated for photons traversing an asymmetrical double slit and the special results are discussed.
