使用有限差分法來計算一些導體與電介質之可極化性

Abstract

使用簡單的有限差分法來計算在圓與圓柱座標系中導體和介電質在不同的形狀的可極化性。在導體和電介質的球與導體和電介質的環中，這個方法所求得的數值之結果與解析的解呈現高度的一致性。然後應用這個方法在半導體截面為眼型的量子環，而這個部份目前尚無可極化性的解析公式。

A simple finite difference method is proposed for calculating polarizability of conductors and dielectrics in various shapes in radial and cylindrical coordinates. Numerical results of this method show good agreement with the analytical solutions of the polarizability of conducting or dielectric sphere and torus. The method is then applied to a semiconductor quantum ring with an eye-shaped cross section for which an analytical formula of porlarizability is not available.