利用蒙地卡羅方法研究波粒二重性

Abstract

本論文首先利用蒙地卡羅方法經由亂數產生器找出π值、利用隨機灑點繪出碎形圖案。然後為了探討波動與粒子的特性，先利用半古典的方式計算出單狹縫與雙狹縫在屏幕上的動量分佈。然後再利用蒙地卡羅方法模擬電子在一維空間隨機通過單狹縫及雙狹縫，觀察其在不同距離後屏幕上形成的圖形，並且與波動方法形成的干涉圖形做比較。進而推廣至二維空間單狹縫及雙狹縫的電子隨機分佈圖形，最終使電子通過任意形狀的孔洞，觀察其最後干涉的結果。接著利用帶相位粒子經圓柱形波導管後因軌跡差而形成的相位疊加，成功重建實驗所得的成像圖案。

This paper used the Monte Carlo method to find out π by random number generator. In order to investigate the characteristics of the wave and particle, semi-classical way is used to calculate the momentum distribution of a single slit and double-slit on the screen. Monte Carlo method is used to simulate electrons randomly passing through a single slit and double slit in one-dimensional space. Graphics formed at different distances on the screen are observed and compared with the interference pattern formed by the wave method. The research is extended to two-dimensional space of a single slit and double slit, and observed the results of the interference patterns. Finally, particles with a phase passed through the cylindrical waveguide resulted to relative phase overlap by trajectory difference and successful reconstructions of the experimental imaging patterns are formed.