等效電路法與k-矩陣法在量子力學之探討｜國立中央大學博碩士論文系統

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研究生：	彭俊傑 Jyun-Jie Pon
論文名稱：	等效電路法與k-矩陣法在量子力學之探討 Quantum-Mechanic Simulation using Equivalent-Circuit Method and k-matrix Method
指導教授：	蔡曜聰 Yao-Tsung Tsai
口試委員:
學位類別：	碩士 Master
系所名稱：	資訊電機學院 - 電機工程學系 Department of Electrical Engineering
畢業學年度：	94
語文別：	英文
論文頁數：	41
中文關鍵詞：	薛丁格波動方程式、量子力學
外文關鍵詞：	Schrödinger wave equation, KP-model, quantum mechanical
相關次數：	點閱：11 下載：0
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我們在論文裡將使用兩種方法來模擬量子力學的系統。第一種方法被稱做k矩陣法，另一個方法則是等效電路法。我們使用這兩種方式來分析周期性的KP-model與非週期性的量子力學系統，由這兩種方式所得到的結果就是薛丁格波動方程式的波函數。另外，我們比較k矩陣法與等效電路法並且得到相同的結果，而我們也會說明這兩種方法的優點與缺點。

In the thesis, we will use two methods to simulate the quantum mechanical systems. The first way is called the k-matrix method, and the other way is the equivalent-circuit method. We use these two methods to analyze periodic KP-model and non-periodic QM systems. The result obtained by these ways is the wave function of the Schrödinger wave equation. Additionally, we will compare the k-matrix method with the equivalent-circuit method and show these results of the k-matrix method are same as the equivalent-circuit method. We will also show the advantages and disadvantages of these two methods.

Contents
Introduction …………………………………………………………………………1
Two Solvers for Solving Schrödinger Equations………………………………3
1	Introduction …………………………………………………………………3
2	Equivalent-Circuit Model of Schrödinger Wave Equation……………4
3	The k-Matrix Method for Simultaneous Complex Equations …………7
4  The Splitting of Energy Level in Quantum Well………………………8
Simulation of Periodic Kronig-Penney Model…………………………………11
1	Introduction of KP-Model…………………………………………………11
2 Simulation Result of k-Matrix Method…… ……………………………16
3 Simulation Result of Equivalent-Circuit Method ……………………19
4 Discussion of Two Solvers…………………………………………………23
Simulation of Non-periodic Quantum Mechanics………………………………25
1 Simulation Result of a Potential Barrier ……………………………25
2 Simulation Result of One-Dimensional Well of Finite Depth………31
3 2-Dimentional Infinite Quantum Well……………………………………37
Conclusion……………………………………………………………………………40
List of Reference……………………………………………………………………..41

                                

Reference
[1] C. H. Kao, “An equivalent circuit model of quantum mechanics and its investigation to device simulation,” M. S. Thesis, Institute of EE, National Central University, Taiwan, Republic of China, Jun. 2004.
[2] J. W. Lee, “An equivalent circuit model for decoupled method in semiconductor device simulation,” M. S. Thesis, Institute of EE, National Central University, Taiwan, Republic of China, Jun. 2002.
[3] C. L. Teng, “An equivalent circuit approach to mixed-level device and circuit simulation,” M. S. Thesis, Institute of EE, National Central University, Taiwan, Republic of China, Jun. 1997.
[4] J. P. Mckelvey, Solid State and Semiconductor Physics, Chapter 4, 6, Robert E. Krieger, Inc., 1966.
[5] C. L. Lin, Modern Physics: Introduction of Solid State Physics, Chapter 5, Wu Nan, Inc., 2004.
[6] B. Arthur, Concepts of Modern Physics, New York: McGraw-Hill, 1995.
[7] A. K. Ghatak, K. Thyagarajan, M. R. Shenoy “A novel numerical technique for solving the one-dimentional Schrödinger equation using matrix approach-application to quantum well structures,” IEEE Journal on Quantum Electronics, vol.24, p.1524-1531, 1988.
[8] N. Zettili, Quantum mechanics : concepts and applications, New York : Wiley, 2001.

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