此篇論文提供了一個有效率的方法去算量子的能階分布.我們用了一種和接觸面相似的網格作為其中之一的座標系統,再用此網格轉換成另一種座標系統,兩種座標系統在用weight function融合後去作離散. 而離散之後所形成的矩陣會為對稱正定矩陣.最後再使用Jacobi-Davidson 的方法算其特徵值以及特徵向量.且所算出的特徵值會有二階精度.

Abstract
We present a simple and efficient numerical method for calculating bound state energies and their corresponding wave function of a axisymmetric 3D QD model. The Schrodinger equation of the model is discretized by using a body fitting curvilinear coordinate system. The result matrix is symmetric and positive definite. The resulting matrix eigenvalue problem is then solved by using a Jacobi-Davidson based method. The scheme is 2nd order accurate and converges extremely fast.

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