在這篇論文中，主要是探討在一維和二維之時空下，薛丁格方程的散射現象。有別於三維和三維以上的Morawetz estimate，我們特別利用對原方程乘上特定權重函數的調整，並進一步獲得一些重要的正項與消去不必要的函數。
接著，我們延續Bourgain 的想法，在整個非線性解局部能量聚集的情況下，可以進一步分離在時間端點非線性解與線性解之能量關係，透過這個方式，藉由對能量歸納法的證明，我們最終能證明非線性解所需要的全域估計。

In this paper, we mainly discuss the scattering phenomenon of Schrodinger Equation in dimension one and two. Being different with the Morawetz estimate of three dimension and above, we multiplied with a specific weight function to the equation and further obtains some importantly positive terms and eliminated the nonessential functions.
Next, we continued Bourgain’s idea in entire nonlinear solution localized energy accumulation situation, we can separate the energy in time vertex between the relationship of nonlinear and linear solution. By this way, we used the induction on the energy size, we obtain the global estimate for the nonlinear solutions of asymptotic completeness in the long run.

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