effective mass 在薛丁格方程式中的電子質量是用非拋物型有效質量近似的方式去模擬單一電子的質量

[PDF]在有效质量近似下，使用线性变分方法计算了处于GaAs ... wulixb.iphy.ac.cn/CN/article/downloadArticleFile.do?... 頁庫存檔 轉為繁體網頁 由 C XI 著作 - ‎1994 - ‎被引用 5 次 - ‎相關文章 1993年4月26日 - 在有效质量近似下，使用线性变分方法计算了处于GaAs-Gal_gALAI 球形量子点中不同. 位置的浅施主杂质的能谱结构，讨论了能级的简并度和不同 ... 非拋物型有效質量近似一維離散薛丁格方程特徵值問題
Authors:	陳信嘉
教師:	林文偉 陳信嘉
Date:	2004
Keywords:	非拋物型有效質量近似 量子井 薛丁格方程 能階 波函數
Abstract:	在這篇論文當中，我們先介紹量子理論的基本物理概念以及量子論的歷史，並且會簡單的介紹薛丁格方程以及量子井。我們藉著離散化一維薛丁格方程式的去做更深入的探討，特別是在薛丁格方程式中的電子質量是用非拋物型有效質量近似的方式去模擬單一電子的質量。在此我們是用central-differencing method 將薛丁格方程離散化，並找到特徵方程式。我們是利用參考文獻（4）的方法，去分析這些方程式的性質，並找到特徵值，在此的特徵值與特徵向量分別代表的是能階與波函數。最後這篇論文的目的，是要找出在量子井內離散能階的個數。 In this paper, we first roughly present the basic physical idea about quantum theory and the history of quantum theory. we will give a simple interpretation of Schr¨odinger equation and illustrate something about quantum well. Furthermore,we investigate the one-dimensional discrete Schr¨odinger equation with Dirichlet boundary conditions. In particular, the mass of a single electron in Schr¨odinger equation is represented by non-parabolic effective mass approximation. Here, we use a central-differencing method to discretize the equations with the uniform mesh size, and we will construct the characteristic equation of this modal problem. As the same skill of this paper [4], we analyze the property of these equations to find the solutions (eigenvalues) of the equations. Here, the eigenvalues and eigenvectors correspond to the energy states and wave functions of the quantum well, respectively. Finally, the aim of this paper is to find out the number of the discrete energy states lying in the well.
Isbasedon:	References [1] David S. Betts and Paul C.W. Davies, Quantum Mechanics, second edition, Chapman and Hall, 1994. [2] Golub, G.H, Some modified matrix eigenvalue problems. SIAM Rev.15, 318-334(1973) [3] Tsung-Min Hwang, Wen-Wei Lin, Jinn-Liang Liu, and Weichung Wang, Numerical computation of cubic eigenvalue problems for a semicnductor quantum dot model with non-parabolic effective mass approximation, 2002, preprint. [4] Wen-Wei Lin, eigenvalue problems for one-dimensional discrete Schr¨odinger opertors with symmetric boundary conditions. SIAM Matrix Anal. Appl., Vol. 23, No. 2 (2001), pp. 524-533. (with J. Juang and S. F. Shieh) [5] Y. Li, J.-L. Liu, O. Voskoboynikov, C. P. Lee, and S. M. Sze. Electron energy level calculations for cylindrical narrow gap semiconductor quantum dot. Comput. Phys.Commun., 140:399V 404, 2001. [6] Serway, Principles of Physics, international edition, Saunders College Publishing, 1994. [7] S. Maimon, E. Finkman, G. Bahir, S. E. Schacham, J. M. Garcia, and P. M. PetroR. Intersublevel transitions in InAs/GaAs quantum dots infrared photodetectors.Appl. Phys. Lett., 73:2003V2005, 1998.
URI:	http://nthur.lib.nthu.edu.tw/handle/987654321/35812
Source:	http://thesis.nthu.edu.tw/cgi-bin/gs/hugsweb.cgi?o=dnthucdr&i=sGH000893214.id
Appears in Collections:	[數學系] 博碩士論文