Chan Chung Ning. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [86]-88). / Text in English; abstracts in English and Chinese. / Chan Chung Ning. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.xi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Classical chaos and quantum chaos --- p.1 / Chapter 1.2 --- Motivations --- p.2 / Chapter 1.3 --- Structure of our study --- p.3 / Chapter Chapter 2. --- Integrability of Hamiltonian Systems --- p.5 / Chapter 2.1 --- Integrable systems --- p.5 / Chapter 2.2 --- KAM perturbation and Poincare surface section --- p.8 / Chapter 2.3 --- Surface sections of Robnik Billiards --- p.11 / Chapter 2.4 --- Linking classical and quantum chaos --- p.16 / Chapter Chapter 3. --- Constraint Operator Method --- p.18 / Chapter 3.1 --- Two-dimensional billiards --- p.18 / Chapter 3.2 --- Formalism of the constraint operator method with the Dirichlet boundary conditions --- p.19 / Chapter 3.3 --- Numerical results: eigenvalues of billiards --- p.24 / Chapter 3.4 --- Discussion on the constraint operator method --- p.29 / Chapter Chapter 4. --- The COM with the Neumann Boundary Conditions --- p.32 / Chapter 4.1 --- Formalism --- p.32 / Chapter 4.2 --- Numerical results --- p.35 / Chapter 4.3 --- Discussion --- p.38 / Chapter Chapter 5. --- Boundary Integral Method --- p.40 / Chapter 5.1 --- Introduction --- p.40 / Chapter 5.2 --- Berry's formalism --- p.41 / Chapter 5.3 --- A modified formalism --- p.46 / Chapter 5.4 --- Numerical results --- p.47 / Chapter 5.5 --- Discussion on the BIM --- p.53 / Chapter Chapter 6. --- Further Discussions on the BIM --- p.55 / Chapter 6.1 --- The choice of the Green's function --- p.55 / Chapter 6.2 --- Principal value --- p.58 / Chapter Chapter 7. --- Conformal Mapping Method --- p.64 / Chapter 7.1 --- Formalism --- p.64 / Chapter 7.2 --- Numerical results --- p.69 / Chapter 7.3 --- Summary --- p.73 / Chapter Chapter 8. --- Spectral Statistics --- p.76 / Chapter 8.1 --- Introduction --- p.76 / Chapter 8.2 --- Numerical results --- p.78 / Chapter 8.3 --- Summary --- p.80 / Chapter Chapter 9. --- Conclusion --- p.83 / Bibliography --- p.86
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322802 |
| Date | January 1999 |
| Contributors | Chan, Chung Ning., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, x, 88 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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