Abstract
本論文中我們處理了一維玻色氣體在無限深方勢阱內有Delta函數作用力 的問題；我們解出了此系統中波函數、能譜、基態能量以及其它熱力學性 質。首先我們在第二章處理了無限深方勢阱內自由粒子與點缺陷以 Delta 函數的位能作用的問題作為比較，而我們發現微擾方法是一個好的 近似結果。其次我們假設在無限深方勢阱內玻色氣體以Delta函數的位能 來互相作用，解出了此系統的玻函數以及能譜。第三章我們處理了兩個玻 色子的問題，第四章則推廣此結果到多個玻色子問題。而當我們取熱力學 極限時，得到了和用週期性邊界條件下相同的結果。 One-dimensional bosons with a delta function interaction in an infinite well is analyzed. Its wave function, energy spectrum, and other thermodynamic properties are obtained. First, for comparison, we deal with the problem that iti- nerant particles interact with a point defect via a delta function interaction in an infinite well in chapter 2, and we find perturbation results to be a good approximation. Secondly, we suppose that the bose gas interact with a delta function interaction in an infinite well, and then we analyze the wavefunction and spectrum. In chapter 3 we deal with two bosons case, and in chapter 4 we generalize the re- sults to many bosons. When we take the thermodynamic limit, we get the results which are the same as those employed by the periodic boundary condition.