在這篇文章中，主要研究的是量子物理中的玻色─愛因斯坦凝聚現象(堅稱為玻愛凝聚)在磁場中的作用，研究方法為數值模擬。玻愛凝聚現象是指在絕對零度時，所有氦原子都會凝聚到一個單一的最低能階(ground state)上。在文章的開頭，先介紹了玻愛凝聚現象以數學來表示即為著名的薛丁格方程式，它是描述電子在原子尺度上的運動方程式。而本文章只研究兩種不同原子在磁場中的作用結果為何，並分別以兩個薛丁格方程式來代表。在序言中，先開門見山的指明了此文章研究的方程式，並說明學者們在玻愛凝聚現象研究的成果有哪些，接著將本文章所研究帶有磁場的薛丁格方程式化簡後並做離散化，離散化的細節與程式碼的撰寫，在第二章中有詳細的介紹。在此文章用的數值方法為局部延續法(local continuation method)，由兩部分組成，第一部份為預測(predictor)而第二部份為修正(corrector)。將局部延續法應用在離散化的薛丁格方程式後，主要問題就變成我們面臨了要解一個大型稀疏矩陣的線性系統。我們利用自然疊代法先找到ㄧ個當磁場為零時的ㄧ個解，並採用1993年所發表的fortran套裝程式BICGSTAB來解決在局部延續法出現的解現性系統的問題，最後，說明本文章的研究結果為何，並以圖表示之。

In this thesis, we use local continuation method to study a two-component Bose-Einstein condensate (BEC) in magnetic field numerically. First, we show the discretized process of a two-component BEC in magnetic field that is the
time-independent coupled nonlinear Schrodinger equation. Second, we present the algorithm and the numerical results.

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