等效質量隨位置變化的問題(Position-dependent effective mass, PDEM) 對於認識延伸WKB近似法在半導體異質接面的束縛態計算上是非常重要的。藉由研究某些典型的問題，我們展現對於束縛態電子而言，延伸的WKB近似法提供了良好的能階近似值。另外，在處理等效質量隨位置變化的問題（PDEM)上，我們的工作也討論並研究了有效質量分佈及位能障對PDEM問題的影響。結果顯示在PDEM問題上精密度會受到有效質量及位能障的影響。

The position-dependent effective mass (PDEM) problem is of enormous importance to the realization of the extended Wentzel-Kramers-Brillouin (WKB) approximation in bound state calculations for semiconductor heterostructures. By studying some model problems, we show that the extended WKB method provides good approximations for the bound states with the high eigenenergies. In addition, the effect of the smoothness of the effective mass distribution functions and potential barrier in the PDEM problems is discussed in our work. We found the precision can be affected by the effective mass and potential barrier in the PDEM.

目 錄
摘要 I
Publications III
目錄 IV
圖次表 VI
第一章 研究背景 1
第二章 量子計算的方法學 3
2-1 WKB近似法 3
2-2 連結方程式 4
2-3 傳輸矩陣法 9
2-4 利用傳輸矩陣法尋找特徵能量 16
2-5 連結傳輸矩陣法與WKB近似法 17
第三章 研究案例 21
3-1 具有空間變化質量的有限深度量子井的問題的解答推導 21
3-2 質量具有階梯型空間分佈的無限深量子井的問題解答推導 31
第四章 計算結果 33
4-1 第一組數據 34
4-2 第二組數據 36
4-3 第三組數據 38
4-4 第四組數據 40
4-5 第五組數據 42
4-6 波函數的圖形 44
第五章 結論 69
參考文獻 71
附錄 73
附錄一 88

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