具陷阱勢能之非線性薛丁格方程組的可壓縮與不可壓縮極限

Abstract

本篇論文是以先前論文中的非線性薛丁格方程組來添加陷阱勢能，再利用其方程組推測其可壓縮與不可壓縮極限會受到什麼影響。我們驗證主要的想法是定義一個``H函數'，加上證明一些守恆律，代換之後再做計算便可得到結果。 本篇論文分為四節。第一節，將所參考文獻中之原式提出並做修改；並以增加一項變數(陷阱勢能)來討論是否會得出相近結果，再將其結果寫出。第二節，證明守恆定律，並利用此結果在第三、第四節證明兩個主要的定理。

We add the trap potentials based on coupled systems of nonlinear Schrodinger equation in the previous paper, and use these to conjecture possible effect of compressible and incompressible limits. The main idea of our arguments is to define an ``H-function', to prove some conservation laws, and to calculate for result after substitution. There are four sections in this paper. In Section 1, we write the equations discussed in the main bibliography. Moreover, we discuss the result after adding one term(trap potential), and conclude the outcome. In Section 2, we prove some conservation laws. According to these,we prove the two main theorem in Section 3 and Section 4.