General time-dependent harmonic oscillator in classical and quantum mechanics : a systematic treatment 古典および量子力学における一般的な時間依存性をもつ調和振動子 : その系統的取扱法
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Bibliographic Information
- Title
-
General time-dependent harmonic oscillator in classical and quantum mechanics : a systematic treatment
- Other Title
-
古典および量子力学における一般的な時間依存性をもつ調和振動子 : その系統的取扱法
- Author
-
金杉, 弘隆
- Author(Another name)
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カナスギ, ヒロタカ
- University
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東京工業大学
- Types of degree
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博士 (理学)
- Grant ID
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乙第3018号
- Degree year
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1997-03-31
Note and Description
博士論文
Table of Contents
- 論文目録 / (0002.jp2)
- Abstract / p2 (0004.jp2)
- Contents / p3 (0005.jp2)
- 1 Introduction / p5 (0007.jp2)
- 2 Classical Mechanics / p10 (0012.jp2)
- 2.1 The equation of motion of harmonic oscillator / p10 (0012.jp2)
- 2.2 Ambiguousness of the Lagrangian / p12 (0014.jp2)
- 2.3 General time-dependent harmonic oscillator / p17 (0019.jp2)
- 2.4 The symmetry of the equation of motion ― Lie's approach / p24 (0026.jp2)
- 2.5 The symmetry of action ― Noether type approach / p31 (0033.jp2)
- 3 Quantum Mechanics / p37 (0039.jp2)
- 3.1 Non-uniqueness of quantization rule / p37 (0039.jp2)
- 3.2 Analytical solution of the simple harmonic oscillator / p40 (0042.jp2)
- 3.3 Husimi's method / p42 (0044.jp2)
- 3.4 Lewis-RiesenfeId's method / p44 (0046.jp2)
- 3.5 General time-dependent harmonic oscillator / p46 (0048.jp2)
- 3.6 Symmetry of Hamiltonian of quantum harmonic oscillator / p52 (0054.jp2)
- 4 Conclusion / p55 (0057.jp2)
- A Kobussen's derivation of inequivalent Lagrangian / p58 (0060.jp2)
- B The Pinney equation / p61 (0063.jp2)
- C The Lie's theory of the symmetry group / p64 (0066.jp2)
- D Summary of some obtained results in §2.4 / p65 (0067.jp2)
- E Summary of some obtained results in §2.5 / p70 (0072.jp2)
- F The algebras su(2) and su(1,1) ― A résumé ― / p75 (0077.jp2)
- G The algebra A₃(su(3)) / p78 (0080.jp2)
- H Table / p80 (0082.jp2)
- I The motion of wave packets / p82 (0084.jp2)
- J The phase space pictures of the damped harmonic oscillator / p90 (0092.jp2)
- K The bound atates of the linear well and the inverse-square well / p94 (0096.jp2)