黎曼空間及橢圓函數的理論及薛丁格方程的應用

The Theory of Riemann Surfaces and Elliptic Functions with application to Nonlinear Schrodinger Equation

戴天恩(Tien-En Tai)

指導教授 ： 蔡孟傑

國立清華大學/理學院/數學系/碩士(2013年)

https://doi.org/10.6843/NTHU.2013.00200

摘要

此論文，我們討論黎曼空間的理論及在黎曼空間上積分的計算，接著討論橢圓函數。
最後，利用這兩個理論討論非線性薛丁格方程的特殊解。

關鍵字

薛丁格方程 ； 黎曼空間 ； 橢圓函數

並列摘要

In this paper, we study the theory of Riemann Surfaces of genus N and the numerical computation of path integrals on those Riemann Surfaces. We then study the classical theory of the elliptic functions.
Finally, we apply both theorys to solve some special solutions of Nonlinear Schrodinger Equation.

參考文獻

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