Inverse problems in scattering: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1993
|
| Series: | Solid mechanics and its applications
23 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 361 S. graph. Darst. |
| ISBN: | 0792324781 |
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| 245 | 1 | 0 | |a Inverse problems in scattering |b an introduction |c by G. M. L. Gladwell |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1993 | |
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| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
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Record in the Search Index
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| adam_text | INVERSE PROBLEMS IN SCATTERING AN INTRODUCTION BY G. M. L. GLADWELL
UNIVERSITY OF WATERLOO, DEPARTMENT OF CIVIL ENGINEERING, WATERLOO,
CANADA KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON TABLE OF
CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . IX 1 SOME SIMPLE WAVE PHENOMENA . . . . . . . . . . . .
. . . . . . . . . 1 1.1 WAVES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 1 1.2 GENERALIZED FUNCTIONS . . . . . . . . . . .
. . . . . . . . . . . . 10 1.3 LOSSLESS TRANSMISSION LINES . . . . . . .
. . . . . . . . . . . . . 15 1.4 WAVES IN AN ELASTIC MEDIUM 16 1.5 SOUND
WAVES 18 1.6 REFLECTION AND TRANSMISSION OF WAVES . 23 1.7 STANDARDISING
THE WAVE EQUATIONS 27 1.8 STANDARDISED REFLECTION AND TRANSMISSION 33
1.9 CONSERVATION EQUATIONS 39 1.10 DIFFERENCE SCHEMES FOR WAVE PROBLEMS
. . . . . . . . . . . . . . 40 1.11 DOWN-UP DIFFERENCE SCHEMES . . . . .
. . . . . . . . . . . . . 46 1.12 CAUSAL SOLUTIONS, GREEN S FUNCTIONS
AND Z-TRANSFORMS . . . . . . 48 2 LAYER-PEELING METHODS FOR DISCRETE
INVERSE PROBLEMS . . . . . . . . . 55 2.1 INTRODUCTION 55 2.2 ON THE
INTERPRETATION OF THE DISCRETE EQUATIONS 59 2.3 THE IMPULSE RESPONSE AND
THE PROPAGATION OF THE WAVEFRONT . . 60 2.4 DISCRETE EQUATIONS FOR
LAYER-PEELING METHODS 63 2.5 SOME QUESTIONS 67 2.6 FUNCTIONS OF A
COMPLEX VARIABLE 67 2.7 SCHUR S LEMMA 71 2.8 THE SCHUR ALGORITHM AND
DOWNWARD CONTINUATION 74 2.9 THE SCHUR ALGORITHM AND TOEPLITZ MATRICES
80 2.10 LAYERED MEDIA OF NON-GOUPILLAUD TYPE 86 3 THE INVERSION OF
DISCRETE SYSTEMS USING NON-CAUSAL SOLUTIONS . . . . 91 3.1 INTRODUCTION
91 3.2 SOME SIMPLE NON-CAUSAL SOLUTIONS 92 3.3 CLAERBOUT S EQUATION . .
. . . . . . . . . . . . . . . . . . . . . . 96 3.4 LEVINSON S ALGORITHM
. . . . . . . . . . . . . . . . . . . . . . . . 97 3.5 LEVINSON S
ALGORITHM AND CLAERBOUT S EQUATION 101 VI TABLE OF CONTENTS 3.6 A
DISCRETE GEPFAND-LEVITAN EQUATION 103 3.7 BRUCKSTEIN AND KAILATH S
EQUATION 106 3.8 TIME-SUMS OF THE BASIC SOLUTIONS ILL 3.9 A DISCRETE
GOPINATH-SONDHI EQUATION 115 3.10 COMMENTS ON THE LITERATURE 119 4 WAVES
IN NON-UNIFORM MEDIA 123 4.1 INTRODUCTION 123 4.2 CHARACTERISTICS 123
4.3 CAUSALITY, INITIAL VALUE PROBLEMS AND INTERVALS OF DEPENDENCE . 128
4.4 RIEMANN S REPRESENTATION 131 4.5 DIFFERENCE SCHEMES FOR
INITIAL-VALUE PROBLEMS 133 4.6 INITIAL-VALUE-BOUNDARY-VALUE PROBLEMS 135
4.7 THE PROPAGATION OF SINGULARITIES 138 5 THE INVERSION OF CONTINUOUS
SYSTEMS USING CAUSAL SOLUTIONS . . . . 147 5.1 INTRODUCTION 147 5.2
RECONSTRUCTION OF THE IMPEDANCE 149 5.3 RECONSTRUCTION OF THE REFLECTION
FUNCTION 150 5.4 A NON-LINEAR INTEGRAL EQUATION FOR THE REFLECTION
FUNCTION . . 152 6 INVERSION OF CONTINUOUS SYSTEMS USING NON-CAUSAL
SOLUTIONS . . . . 157 6.1 INTRODUCTION 157 6.2 THE BASIC SOLUTIONS 157
6.3 SOME GENERAL INTEGRAL EQUATIONS 161 6.4 KREIN S INTEGRAL EQUATION
163 6.5 THE LEVINSON-DURBIN ALGORITHM 169 6.6 THE LINEAR GEL FAND
LEVITAN INTEGRAL EQUATION 172 6.7 THE NON-LINEAR GEPFAND-LEVITAN
EQUATION 178 6.8 THE MARCHENKO INTEGRAL EQUATION 181 6.9 THE
GOPINATH-SONDHI EQUATION 182 7 AN INTRODUCTION TO THE INVERSE SCATTERING
PROBLEM OF QUANTUM THEORY 189 7.1 INTRODUCTION 189 7.2 SCHROEDINGER S
EQUATION 190 7.3 ORTHOGONAL POLYNOMIALS 191 7.4 THE SPECTRAL PROBLEM FOR
A JACOBI MATRIX 195 7.5 FUNCTIONS OF A COMPLEX VARIABLE*II 201 7.6
FOURIER S PROBLEM 211 7.7 A FINITE-DIFFERENCE FORM OF THE SCHROEDINGER
EQUATION 220 7.8 A FINITE-DIFFERENCE FORM OF THE *-MATRIX APPROACH 232
7.9 THE DETERMINATION OF THE JOST FUNCTION 233 7.10 THE GEL FAND LEVITAN
PROCEDURE FOR JACOBI MATRICES 237 7.11 THE GEPFAND-LEVITAN PROCEDURE 241
7.12 THE MARCHENKO PROCEDURE 242 7.13 SOME GENERALIZATIONS 246 TABLE OF
CONTENTS VII 8 THE SCHROEDINGER EQUATION ON THE HALF LINE 251 8.1
INTRODUCTION 251 8.2 THE SCHROEDINGER EQUATION ON THE FINITE LINE 251 8.3
THE SPECTRUM FOR THE FINITE LINE IS DISCRETE 257 8.4 SCHROEDINGER S
EQUATION ON THE HALF LINE: THE DISCRETE SPECTRUM 261 8.5 THE REGULAR
SOLUTION 268 8.6 THE JOST SOLUTION 270 8.7 THE JOST FUNCTION AND THE
PHASE SHIFT 273 8.8 THE BOUND STATES 276 8.9 THE INTEGRAL REPRESENTATION
OF THE JOST FUNCTION 280 8.10 THE ORTHOGONALITY RELATIONS 283 9 THE
LEBESQUE INTEGRAL 289 9.1 INTRODUCTION 289 9.2 REAL AND COMPLEX NUMBERS
290 9.3 METRIC SPACES 292 9.4 FUNCTIONS AND FUNCTION SPACES 295 9.5 THE
RIEMANN INTEGRAL 300 9.6 MEASURABLE SETS AND MEASURABLE FUNCTIONS 303
9.7 THE LEBESGUE INTEGRAL 306 9.8 APPLICATIONS AND PROPERTIES OF THE
LEBESGUE INTEGRAL 310 9.9 DIFFERENTIATION AND INTEGRATION 312 9.10
FOURIER TRANSFORMS 316 10 INVERSE SCATTERING FOR THE SCHROEDINGER
EQUATION 319 10.1 INTRODUCTION 319 10.2 THE POZNER-LEVITAN
REPRESENTATION OF * 321 10.3 THE GEL FAND-LEVITAN INTEGRAL EQUATION 326
10.4 THE LEVIN REPRESENTATION OF THE JOST SOLUTION 328 10.5 THE
MARCHENKO INTEGRAL EQUATION 331 10.6 EQUIVALENCE OF THE EQUATIONS OF
GEL FAND-LEVITAN AND MARCHENKO 334 10.7 CONDITIONS ON THE DATA LEADING
TO A REGULAR POTENTIAL 337 REFERENCES 345 INDEX 355 INDEX OF NOTATIONS
359
|
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| spelling | Gladwell, Graham M. L. Verfasser aut Inverse problems in scattering an introduction by G. M. L. Gladwell Dordrecht u.a. Kluwer 1993 X, 361 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Solid mechanics and its applications 23 Mathematik Inverse problems (Differential equations) Scattering (Mathematics) Scattering (Physics) Mathematics Mechanik (DE-588)4038168-7 gnd rswk-swf Inverses Streuproblem (DE-588)4027547-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Inverses Streuproblem (DE-588)4027547-4 s Mechanik (DE-588)4038168-7 s DE-604 Quantenmechanik (DE-588)4047989-4 s Solid mechanics and its applications 23 (DE-604)BV004342211 23 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006391630&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gladwell, Graham M. L. Inverse problems in scattering an introduction Solid mechanics and its applications Mathematik Inverse problems (Differential equations) Scattering (Mathematics) Scattering (Physics) Mathematics Mechanik (DE-588)4038168-7 gnd Inverses Streuproblem (DE-588)4027547-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4027547-4 (DE-588)4047989-4 |
| title | Inverse problems in scattering an introduction |
| title_auth | Inverse problems in scattering an introduction |
| title_exact_search | Inverse problems in scattering an introduction |
| title_full | Inverse problems in scattering an introduction by G. M. L. Gladwell |
| title_fullStr | Inverse problems in scattering an introduction by G. M. L. Gladwell |
| title_full_unstemmed | Inverse problems in scattering an introduction by G. M. L. Gladwell |
| title_short | Inverse problems in scattering |
| title_sort | inverse problems in scattering an introduction |
| title_sub | an introduction |
| topic | Mathematik Inverse problems (Differential equations) Scattering (Mathematics) Scattering (Physics) Mathematics Mechanik (DE-588)4038168-7 gnd Inverses Streuproblem (DE-588)4027547-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Mathematik Inverse problems (Differential equations) Scattering (Mathematics) Scattering (Physics) Mathematics Mechanik Inverses Streuproblem Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006391630&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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