Lau Ching Yan Ada = 耗散系統中的廣義Sturm-Liouville理論 / 劉正欣. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 156-157). / Text in English; abstracts in English and Chinese. / Lau Ching Yan Ada = Hao san xi tong zhong de guang yi Sturm-Liouville li lun / Liu Zhengxin. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Vibrational motion in physics --- p.1 / Chapter 1.2 --- Normal modes of vibration --- p.2 / Chapter 1.3 --- Boundary conditions --- p.4 / Chapter 1.4 --- The wave equation --- p.6 / Chapter 1.4.1 --- Mechanical waves --- p.7 / Chapter 1.4.2 --- Electromagnetic waves --- p.9 / Chapter 1.5 --- General form of the wave equation --- p.10 / Chapter 1.5.1 --- V(x) as a restoring force --- p.11 / Chapter 1.5.2 --- V(x) in gravitational waves --- p.13 / Chapter 1.5.3 --- V(x) by transformation --- p.16 / Chapter 2 --- Sturm-Liouville systems --- p.18 / Chapter 2.1 --- Introduction --- p.18 / Chapter 2.2 --- Differential operators --- p.19 / Chapter 2.2.1 --- Introduction --- p.19 / Chapter 2.2.2 --- Adjoint operators --- p.20 / Chapter 2.2.3 --- Self-adjoint operators --- p.21 / Chapter 2.2.4 --- More examples --- p.24 / Chapter 2.3 --- Sturm-Liouville boundary-value problems --- p.27 / Chapter 2.4 --- Sturm-Liouville theory --- p.28 / Chapter 2.4.1 --- Real eigenvalues --- p.29 / Chapter 2.4.2 --- Orthogonal eigenfunctions --- p.30 / Chapter 2.4.3 --- Completeness of eigenfunctions --- p.31 / Chapter 2.4.4 --- Interlacing zeros of the eigenfunctions --- p.33 / Chapter 2.5 --- Applications of Sturm-Liouville theory --- p.35 / Chapter 2.5.1 --- Vibrations of a string --- p.36 / Chapter 2.5.2 --- The hydrogen atom --- p.40 / Chapter 3 --- Wave equation with damping --- p.46 / Chapter 3.1 --- Statement of problem --- p.46 / Chapter 3.1.1 --- The equation --- p.46 / Chapter 3.1.2 --- The operator --- p.48 / Chapter 3.1.3 --- Non-self-adjointness --- p.49 / Chapter 3.2 --- Eigenfunctions and Eigenvalues --- p.51 / Chapter 3.3 --- The completeness problem --- p.53 / Chapter 4 --- Green's function solution --- p.55 / Chapter 4.1 --- Introduction --- p.55 / Chapter 4.2 --- Green's function solution --- p.56 / Chapter 4.3 --- Fourier transform --- p.58 / Chapter 4.4 --- Inverse Fourier transform --- p.61 / Chapter 5 --- Proof of completeness --- p.66 / Chapter 5.1 --- WKB approximation --- p.66 / Chapter 5.2 --- "An upper bound for \G(x,y,w)e~iwt\ " --- p.68 / Chapter 5.3 --- Proof of completeness --- p.72 / Chapter 5.3.1 --- The limit when R→∞ --- p.72 / Chapter 5.3.2 --- Eigenfunction expansion --- p.76 / Chapter 6 --- The bilinear map --- p.80 / Chapter 6.1 --- Introduction --- p.80 / Chapter 6.2 --- Evaluation of J1(wj) --- p.82 / Chapter 6.3 --- Self-adjointness of H --- p.84 / Chapter 6.4 --- Properties of the map --- p.87 / Chapter 7 --- Applications --- p.89 / Chapter 7.1 --- Eigenfunction expansion --- p.89 / Chapter 7.2 --- Perturbation theory --- p.94 / Chapter 7.2.1 --- First and second-order corrections --- p.95 / Chapter 7.2.2 --- Example --- p.97 / Chapter 7.2.3 --- Example (Constant r) --- p.102 / Chapter 8 --- Critical points --- p.104 / Chapter 8.1 --- Introduction --- p.104 / Chapter 8.2 --- Conservative cases (Γ = 0) --- p.105 / Chapter 8.3 --- Non-conservative cases (Constant r) --- p.107 / Chapter 8.4 --- Critical points away from imaginary axis --- p.108 / Chapter 9 --- Jordan block and applications --- p.114 / Chapter 9.1 --- Jordan basis --- p.114 / Chapter 9.2 --- An analytical example --- p.117 / Chapter 9.2.1 --- Solving for the extra basis function --- p.117 / Chapter 9.2.2 --- Freedom of choice --- p.118 / Chapter 9.2.3 --- Interpolating function --- p.120 / Chapter 9.3 --- A numerical example --- p.122 / Chapter 9.3.1 --- "Solving for f2,1 " --- p.124 / Chapter 9.3.2 --- Interpolating function --- p.126 / Chapter 9.4 --- Jordan basis expansion --- p.127 / Chapter 9.5 --- Perturbation theory near critical points --- p.131 / Appendices --- p.142 / Chapter A --- WKB approximation --- p.142 / Chapter B --- Green's function (Discontinuous V(x)) --- p.145 / Chapter B.l --- Finite discontinuouity in V(x) --- p.145 / Chapter B.1.1 --- Green's function --- p.145 / Chapter B.1.2 --- "Behaviour of the extra phases Φ, Φ " --- p.147 / Chapter B.2 --- Delta function in --- p.148 / Chapter B.2.1 --- Green's function --- p.148 / Chapter B.2.2 --- "Behaviour of the extra phases Φ, Φ " --- p.150 / Chapter C --- Dual basis --- p.151 / Chapter C.1 --- Matrix representation --- p.152 / Chapter C.2 --- Relation with bilinear map --- p.153 / Chapter C.3 --- Construction of dual basis --- p.154 / Bibliography --- p.156
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324784 |
| Date | January 2004 |
| Contributors | Lau, Ching Yan Ada., 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, xi, 157 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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