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系統識別號 U0026-1507201314415700
論文名稱(中文) 在緩慢變化中近似方法的探討
論文名稱(英文) Critical Study on Adiabatic Approximation
校院名稱 成功大學
系所名稱(中) 物理學系碩博士班
系所名稱(英) Department of Physics
學年度 101
學期 2
出版年 102
研究生(中文) 杜氏娥
研究生(英文) Thi-Nga Do
學號 L26007038
學位類別 碩士
語文別 英文
論文頁數 47頁
口試委員 指導教授-陳家駒
口試委員-蔡錦俊
口試委員-包健華
中文關鍵字 none 
英文關鍵字 adiabatic approximation  adiabatic condition  two-level systems 
學科別分類
中文摘要 none
英文摘要 In this thesis, we would like to study on the consistency of the adiabatic theorem. We analyze and reexamine the validity of the adiabatic approximation, and in particular the necessity and insufficiency of the traditional adiabatic conditions. We will argue that the adiabatic condition is insufficent but it is necessary in guaranteeing the validity of the adiabatic approximation. We also introduce different examples of two-level systems which are exactly solvable to demonstrate the necessity and insufficiency of the adiabatic conditions, as well as the inconsistency of the adiabatic approximation.
論文目次 Chapter 1. Introduction . . . 5
1.1. General Background 5
1.2. Objective of this study . . . . . . . . . 7
Chapter 2. Review on Approximation Methods . 9
2.1. Time-dependent Perturbation Theory . . . . 9
2.1.1. Time-dependent Potentials . . . . . . . . . 9
2.1.2. Time-dependent Perturbation Theory . . . . . . . . 10
2.2. Review on the Adiabatic Theorem . . . . . . 12
Chapter 3. Necessary conditions for the validity of the adiabatic approximation . . .
16
3.1. Derivation of the necessary condition . . . . 17
3.2. Study on a two-level system . . . 18
Chapter 4. Discussion on the consistency of the adiabatic approximation . . . . . 26
4.1. Is the traditional adiabatic condition for non-degenerate Hamiltonian suffi-
cient? . . . . . . . .
27
4.2. Consistency of the adiabatic approximation . . . . . . . 36
Chapter 5. Conclusions . . 44
Reference . . 47
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(2005).
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6. Andris Ambainis and Oded Regev, quant-ph /0411152v2 (2006).
7. Yan Zhao, Phys. Rev. A 77, 032109 (2008).
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(2007).
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