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Spectral inversion problem for conservation and open systems. / 守恆及開放系統的能譜反問題 / Spectral inversion problem for conservation and open systems. / Shou heng ji kai fang xi tong de neng pu fan wen ti

Yip Chi Ming = 守恆及開放系統的能譜反問題 / 葉志明. / Thesis submitted in 2000. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves [244]-247). / Text in English; abstracts in English and Chinese. / Yip Chi Ming = Shou heng ji kai fang xi tong de neng pu fan wen ti / Ye Zhiming. / Abstract --- p.i / Acknowledgements --- p.ii / Contents --- p.iii / List of Figures --- p.viii / List of Tables --- p.xxi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- The Sturm-Liouville Problem --- p.3 / Chapter 1.2 --- Historical review of inverse problems --- p.7 / Chapter 1.3 --- Conservative systems --- p.10 / Chapter 1.4 --- Open systems --- p.10 / Chapter 1.5 --- Organization of the following chapters --- p.11 / Chapter Chapter 2. --- Conservative Spectral Problem --- p.12 / Chapter 2.1 --- The system --- p.12 / Chapter 2.2 --- Properties of conservative systems --- p.13 / Chapter 2.2.1 --- Asymptotic expansion of eigenvalues --- p.14 / Chapter 2.3 --- Forward spectral problem --- p.16 / Chapter 2.3.1 --- FDM and FEM --- p.17 / Chapter 2.3.2 --- Solving transcendental equation --- p.20 / Chapter 2.4 --- Phase shift problem --- p.20 / Chapter 2.4.1 --- Square well potential --- p.22 / Chapter Chapter 3. --- Forward Spectral Problem for Open Systems --- p.25 / Chapter 3.1 --- The system --- p.26 / Chapter 3.2 --- Properties of open systems --- p.28 / Chapter 3.2.1 --- Asymptotic behaviour of QNM eigenvalues --- p.28 / Chapter 3.2.2 --- Doubling of modes --- p.33 / Chapter 3.2.3 --- Generalized norm of QNMs --- p.34 / Chapter 3.2.4 --- Completeness --- p.37 / Chapter 3.2.5 --- Eigenfunction expansion for QNMs - two component formalism --- p.39 / Chapter 3.3 --- Forward spectral problem --- p.45 / Chapter Chapter 4. --- Conservative Inverse Problem --- p.50 / Chapter 4.1 --- Sun-Young-Zou (SYZ) method --- p.51 / Chapter 4.1.1 --- Perturbative inversion --- p.53 / Chapter 4.1.2 --- The regulators (δn) --- p.54 / Chapter 4.1.3 --- Total inversion (TI) --- p.59 / Chapter 4.1.4 --- Numerical results --- p.60 / Chapter 4.2 --- Rundell and Sacks method (RS method) --- p.74 / Chapter 4.2.1 --- Completeness --- p.75 / Chapter 4.2.2 --- The integral equation --- p.78 / Chapter 4.2.3 --- Uniqueness --- p.82 / Chapter 4.2.4 --- RS formalism --- p.84 / Chapter 4.2.5 --- Numerical results and difficulties --- p.89 / Chapter 4.2.6 --- Summary --- p.110 / Chapter 4.3 --- Phase shift problem --- p.112 / Chapter 4.3.1 --- Reduction to spectral problem --- p.113 / Chapter 4.3.2 --- Modified RS algorithm for finite-range phase shift problem --- p.116 / Chapter 4.3.3 --- Discussion --- p.130 / Chapter 4.4 --- Bound states --- p.131 / Chapter Chapter 5. --- Open Inverse Problem --- p.136 / Chapter 5.1 --- SYZ method --- p.136 / Chapter 5.1.1 --- Perturbative Inversion (PI) and Total Inversion (TI) --- p.137 / Chapter 5.1.2 --- Numerical results --- p.138 / Chapter 5.1.3 --- Other choices of (δn) --- p.156 / Chapter 5.2 --- RS method --- p.158 / Chapter 5.2.1 --- The integral equation --- p.159 / Chapter 5.2.2 --- Cauchy data --- p.160 / Chapter 5.2.3 --- Completeness conjecture --- p.162 / Chapter 5.2.4 --- Numerical verification of completeness condition --- p.163 / Chapter 5.2.5 --- Inversion for Cauchy data --- p.166 / Chapter 5.2.6 --- Cauchy data on 0 < x≤ α --- p.167 / Chapter 5.2.7 --- Comparison system --- p.169 / Chapter Chapter 6. --- Conclusions and Further Studies --- p.188 / Chapter 6.1 --- Conclusions of this thesis --- p.188 / Chapter 6.2 --- Further studies --- p.189 / Chapter Appendix A. --- Singular Value Decomposition --- p.199 / Chapter Appendix B. --- Asymptotic Behaviour of Phase Shifts --- p.203 / Chapter B.1 --- Asymptotic behaviour of phase shift data --- p.203 / Chapter B.2 --- Levinson's theorem --- p.204 / Chapter Appendix C. --- Forward Problem for Conservative Systems --- p.207 / Chapter C.1 --- Finite difference method --- p.207 / Chapter C.2 --- Finite element method --- p.209 / Chapter C.2.1 --- Solving transcendental equation --- p.215 / Chapter Appendix D. --- FDM and FEM for Open Systems --- p.220 / Chapter D.1 --- Finite difference method --- p.220 / Chapter D.2 --- Finite element method --- p.222 / Chapter Appendix E. --- Asymptotic Behaviour of NM Eigenvalues --- p.226 / Chapter Appendix F. --- Asymptotic Behaviour of QNM Eigenvalues --- p.232 / Chapter Appendix G. --- QNM Forward Problem 一 Transcendental Equation --- p.239 / Chapter Appendix H. --- Forward Problem - Calculation of Phase Shifts --- p.243 / Bibliography --- p.245

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323509
Date January 2001
ContributorsYip, Chi Ming., Chinese University of Hong Kong Graduate School. Division of Physics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, xx, 247 leaves : ill. ; 30 cm.
RightsUse 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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