Studies on symmetry and bifurcation of the classical and quantized MIC-Kepler problem and Hénon-Heiles system 古典及び量子力学系におけるMIC-ケプラー問題の対称性とヘノン・ハイレス系の分岐に関する研究

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著者

    • 上野, 嘉夫 ウワノ, ヨシオ

書誌事項

タイトル

Studies on symmetry and bifurcation of the classical and quantized MIC-Kepler problem and Hénon-Heiles system

タイトル別名

古典及び量子力学系におけるMIC-ケプラー問題の対称性とヘノン・ハイレス系の分岐に関する研究

著者名

上野, 嘉夫

著者別名

ウワノ, ヨシオ

学位授与大学

京都大学

取得学位

工学博士

学位授与番号

甲第4905号

学位授与年月日

1991-09-24

注記・抄録

博士論文

目次

  1. 論文目録 / (0001.jp2)
  2. CONTENTS / p1 (0006.jp2)
  3. INTRODUCTION / p1 (0008.jp2)
  4. PART I THE SYMMETRY GROUPS OF THE MIC-KEPLER PROBLEM BOTH IN CLASSICAL AND QUANTUM MECHANICS / (0015.jp2)
  5. Chapter1 THE SYMMETRY GROUP OF THE MIC-KEPLER PROBLEM FOR NEGATIVE ENERGIES.CLASSICAL THEORY / (0016.jp2)
  6. 1.1 Introduction / p19 (0017.jp2)
  7. 1.2 Reduction of a phase space([数式],dθ) / p21 (0018.jp2)
  8. 1.3 Reduction of the conformal Kepler problem / p27 (0021.jp2)
  9. 1.4 Negative-energy surfaces for the reduced system / p29 (0022.jp2)
  10. 1.5 The symmetry group of the reduced Hamiltonian system / p31 (0023.jp2)
  11. 1.6 Constants of motion for the reduced Hamiltonian system / p32 (0024.jp2)
  12. References for Chapter1 / p38 (0027.jp2)
  13. Chapter2 THE SYMMETRY GROUP OF THE MIC-KEPLER PROBLEM FOR NEGATIVE ENERGIES.QUANTUM THEORY / (0027.jp2)
  14. 2.1 Introduction / p41 (0028.jp2)
  15. 2.2 A review of the quantized conformal Kepler problem / p45 (0030.jp2)
  16. 2.3 Reduction of L²(R⁴;4rdx) / p46 (0031.jp2)
  17. 2.4 Reduction of the quantized conformal Kepler problem / p52 (0034.jp2)
  18. 2.5 Negative energy eigenspaces of (Tm,Hm) / p53 (0034.jp2)
  19. 2.6 The symmetry group for (Tm,Hm)of negative energy / p55 (0035.jp2)
  20. 2.7 Generators of symmetry group / p59 (0037.jp2)
  21. 2.8 Monopole harmonics / p62 (0039.jp2)
  22. Appendix / p66 (0041.jp2)
  23. References for Chapter2 / p68 (0042.jp2)
  24. Chapter3 THE SYMMETRY GROUPS OF THE MIC-KEPLER PROBLEM FOR ZERO-ENERGY BOTH IN CLASSICAL AND QUANTUM MECHNICS / (0043.jp2)
  25. 3.1 Introduction / p73 (0044.jp2)
  26. 3.2 A review of the U(l) of the four-dimensional conformal Kepler problem.Classical theory / p75 (0045.jp2)
  27. 3.3 A symmetry group of a free particle and its application to the conformal Kepler problem with zero-energy.Classical theory / p77 (0046.jp2)
  28. 3.4 The symmetry group of the MIC-Kepler problem with zero-energy.Classical theory / p80 (0048.jp2)
  29. 3.5 A review of the U(l) of the four-dimensional conformal Kepler problem.Quantum theory / p84 (0050.jp2)
  30. 3.6 A symmetry group of a free particle and its application to the conformal Kepler problem with zero-energy.Quantum theory / p86 (0051.jp2)
  31. 3.7 The symmetry group of the MIC-Kepler problem with zero-energy.Quantum theory / p90 (0053.jp2)
  32. 3.8 Relation to Mackey's induced representation / p94 (0055.jp2)
  33. Appendices / p97 (0056.jp2)
  34. References for Chapter3 / p102 (0059.jp2)
  35. Chapter4 THE SYMMETRY GROUPS OF THE MIC-KEPLER PROBLEM FOR FOR POSITIVE ENERGIES BOTH IN CLASSICAL AND QUANTUM MECHANICS / (0060.jp2)
  36. 4.1 Introduction / p107 (0061.jp2)
  37. 4.2 A review of the U(l) of the four-dimensional conformal Kepler problem.Classical / p109 (0062.jp2)
  38. 4.3 A symmetry group of a free particle and its application to the conformal Kepler problem with positive energies.Classical theory / p111 (0063.jp2)
  39. 4.4 The symmetry group of the MIC-Kepler problem with positive energies.Classical theory / p114 (0065.jp2)
  40. 4.5 A review of the U(l) of the four-dimensional conformal Kepler problem.Quantum theory / p117 (0066.jp2)
  41. 4.6 A symmetry group of the repulsive oscillator and its application to the conformal Kepler problem with positive energies.Quantum theory / p118 (0067.jp2)
  42. 4.7 The symmetry group of the MIC-Kepler problem with positive energies.Quantum theory / p124 (0070.jp2)
  43. 4.8 Relation to the principal series representation of SL(2,C) / p127 (0071.jp2)
  44. Appendices / p129 (0072.jp2)
  45. References for Chapter4 / p133 (0074.jp2)
  46. PART II BIFURCATION IN THE QUANTUM SYSTEM FOR AND APPROXIMATION TO THE HÉNON-HEILES SYSTEM / (0075.jp2)
  47. Chapter5 BIFURCATION IN THE QUANTUM SYSTEM FOR AN APPROXIMATION TO THE HÉNON-HEILES SYSTEM / (0076.jp2)
  48. 5.1 Introduction / p139 (0077.jp2)
  49. 5.2 A review of the Hénon-Heiles system / p144 (0080.jp2)
  50. 5.3 Quantization of the truncated H-H system and the eigenvalue problem (numerical result) / p148 (0082.jp2)
  51. 5.4 The degeneracy of eigenvalues at μ=-1/3 / p150 (0083.jp2)
  52. 5.5 Variation of eigenfunctions / p159 (0087.jp2)
  53. 5.6 Level curve pattern of the density functions / p170 (0093.jp2)
  54. Figures and Tables for Chapter5 / p176 (0096.jp2)
  55. References for Chapter5 / p184 (0100.jp2)
  56. Chapter6 Concluding remarks / [p187] (0101.jp2)
  57. Acknowledgements / p193 (0104.jp2)
  58. List of author's papers cited in this thesis / p194 (0105.jp2)
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  • NII論文ID(NAID)
    500000080703
  • NII著者ID(NRID)
    • 8000000080910
  • DOI(NDL)
  • NDL書誌ID
    • 000000245017
  • データ提供元
    • NDL ONLINE
    • NDLデジタルコレクション

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