Yuen Kwun Wan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves [91]-93). / Text in English; abstracts in English and Chinese. / Yuen Kwun Wan. / Abstract --- p.i / Acknowledgements --- p.ii / Contents --- p.iii / List of Figures --- p.vi / List of Tables --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Formalism of Geometrical Phase --- p.4 / Chapter 2.1 --- Adiabatic cyclic evolution in the parameter space --- p.4 / Chapter 2.2 --- Cyclic evolution of a quantum state on the projective Hilbert space --- p.8 / Chapter 2.3 --- General setting for Berry's phase --- p.11 / Chapter Chapter 3. --- Geometric Phases in Physical Systemms --- p.16 / Chapter 3.1 --- The Aharonov-Bohm Effect --- p.16 / Chapter 3.2 --- An Electron a in Magnetic Field --- p.20 / Chapter 3.2.1 --- The Geometrical Phase in The Adiabatic Limit --- p.22 / Chapter 3.2.2 --- The Geometrical Phases for Other Special Cases --- p.25 / Chapter 3.2.2.1 --- Cyclic Evolution --- p.26 / Chapter 3.2.2.2 --- The Pancharatnam Phase Difference Between ̐ưجψ(t)〉〉〉 and ̐ưجψ(t-pr)〉 --- p.27 / Chapter Chapter 4. --- Review on The Dynamical Cavity Problems --- p.34 / Chapter 4.1 --- Scalar Electrodynamics in a 1-D Cavity with Moving Boundaries --- p.34 / Chapter 4.1.1 --- The Method of Moore's R Function --- p.36 / Chapter 4.1.2 --- Method of Transformation --- p.37 / Chapter 4.2 --- Scalar Electrodynamics in a 1-D Cavity with Oscillating Boundaries --- p.38 / Chapter 4.3 --- Scalar Electrodynamics in a Spherical Cavity with Moving Boundary --- p.39 / Chapter Chapter 5. --- The quantum mechanical phase of a particle in vibrating cavity --- p.41 / Chapter 5.1 --- SU(2) method --- p.48 / Chapter 5.1.1 --- Formalism --- p.48 / Chapter 5.1.2 --- Calculation --- p.51 / Chapter 5.2 --- Rotating Wave Approximation(RWA) --- p.52 / Chapter 5.2.1 --- Formalism --- p.52 / Chapter 5.2.2 --- Behaviors of the system --- p.54 / Chapter 5.2.3 --- Energy --- p.56 / Chapter 5.2.4 --- Geometrical Phases of The System at Resonances --- p.58 / Chapter 5.3 --- Results --- p.63 / Chapter 5.3.1 --- For a Cylindrical Cavity --- p.63 / Chapter 5.4 --- For a Spherical Cavity --- p.70 / Chapter 5.5 --- Conclusion and Discussion --- p.74 / Chapter Chapter 6. --- Summary --- p.76 / Chapter Appendix A. --- Energy Eigenfunctions and Eigenvalues of a Statics Cavity --- p.79 / Chapter A.1 --- For the Case of Cylindrical Cavity --- p.79 / Chapter A.1.1 --- The Energy Eigenfunctions and Corresponding Eigenvalues --- p.81 / Chapter A.2 --- For the Case of Spherical Cavity --- p.81 / Chapter A.2.1 --- The Radial Equation --- p.82 / Chapter A.2.2 --- The Angular Equation --- p.83 / Chapter A.2.3 --- The Energy Eigenfunctions and Corresponding Eigenvalues --- p.84 / Chapter Appendix B. --- The Schrodinger Equation for The Transformed System --- p.85 / Chapter B.1 --- The Schrodinger Equation --- p.85 / Chapter B.2 --- Radial Part of The Schrodinger Equation --- p.86 / Chapter B.2.1 --- For The Case of Cylindrical Cavity --- p.86 / Chapter B.2.2 --- For The Case of Spherical Cavity --- p.87 / Chapter Appendix C. --- Method of Rotating Wave Approximation --- p.88 / Bibliography --- p.91
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323600 |
| Date | January 2001 |
| Contributors | Yuen, Kwun Wan., 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, viii, 93 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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