Multiple scattering in solids:
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York [u.a.]
Springer
2000
|
Schriftenreihe: | Graduate texts in contemporary physics
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Literaturangaben |
Beschreibung: | XIII, 285 S. graph. Darst. |
ISBN: | 038798853X |
Internformat
MARC
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100 | 1 | |a Gonis, Antonios |e Verfasser |4 aut | |
245 | 1 | 0 | |a Multiple scattering in solids |c Antonios Gonis ; William H. Buttler |
264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
300 | |a XIII, 285 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 0 | |a Graduate texts in contemporary physics | |
500 | |a Literaturangaben | ||
650 | 7 | |a Diffusion (physique nucléaire) |2 ram | |
650 | 7 | |a Énergie, Bandes d' (physique) |2 ram | |
650 | 4 | |a Energy-band theory of solids | |
650 | 4 | |a Multiple scattering (Physics) | |
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Datensatz im Suchindex
_version_ | 1804127761615290368 |
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adam_text | ANTONIOS GONIS WILLIAM H. BUTLER MULTIPLE SCATTERING IN SOLIDS WITH 44
ILLUSTRATIONS SPRINGER CONTENTS PREFACE V 1 INTRODUCTION 1 1.1 BASIC
CHARACTERISTICS OF MST 1 1.2 ELECTRONIC STRUCTURE CALCULATIONS 3 1.3 THE
AIM OF THIS BOOK 4 REFERENCES 4 2 INTUITIVE APPROACH TO MST 6 2.1
HUYGENS PRINCIPLE AND MST 6 2.1.1 INFORMAL DISCUSSION: POINT SCATTERERS
7 2.1.2 FORMAL PRESENTATION 12 2.2 TIME-INDEPENDENT GREEN FUNCTIONS 15
REFERENCES 17 3 SINGLE-POTENTIAL SCATTERING 18 3.1 PARTIAL-WAVE ANALYSIS
OF SINGLE POTENTIAL SCATTERING ... 19 3.2 GENERAL CONSIDERATIONS 20 3.3
SPHERICALLY SYMMETRIC POTENTIALS 21 3.3.1 FREE-PARTICLE SOLUTIONS 23
3.3.2 THE RADIAL EQUATION FOR CENTRAL POTENTIALS .... 24 3.3.3 THE
SCATTERING AMPLITUDE 26 3.3.4 NORMALIZATION OF THE SCATTERING WAVE
FUNCTION . . 28 3.3.5 INTEGRAL EXPRESSIONS FOR THE PHASE SHIFTS 29 3.4
NONSPHERICAL POTENTIALS 30 X CONTENTS 3.4.1 ALTERNATIVE FORMS OF THE
SOLUTION 32 3.4.2 DIRECT DETERMINATION OF THE T-MATRIX(*) 34 3.5 WAVE
FUNCTION IN THE MOON REGION 36 3.5.1 DISPLACED-CENTER APPROACH: CONVEX
CELLS 38 3.5.2 DISPLACED-CELL APPROACH: CONVEX CELLS 40 3.5.3 NUMERICAL
EXAMPLE: CONVERGENCE FOR SQUARE CELL . 42 3.5.4 DISPLACED-CELL APPROACH:
CONCAVE CELLS (*).... 44 3.6 EFFECT OF THE POTENTIAL IN THE MOON REGION
47 3.7 CONVERGENCE OF BASIS FUNCTION EXPANSIONS (*) 50 3.7.1 FIRST
JUSTIFICATION 51 3.7.2 SECOND JUSTIFICATION 52 REFERENCES 54 4 FORMAL
DEVELOPMENT OF MST 55 4.1 SCATTERING THEORY FOR A SINGLE POTENTIAL 55
4.1.1 THE S-MATRIX AND THE T-MATRIX 56 4.1.2 T- MATRICES AND GREEN
FUNCTIONS 58 4.2 TWO-POTENTIAL SCATTERING 59 4.2.1 AN INTEGRAL EQUATION
FOR THE I-MATRIX 62 4.3 THE EQUATIONS OF MULTIPLE SCATTERING THEORY 62
4.3.1 THE WAVE FUNCTIONS OF MULTIPLE SCATTERING THEORY 64 4.4
REPRESENTATIONS 68 4.4.1 THE COORDINATE REPRESENTATION 68 4.4.2 THE
ANGULAR-MOMENTUM REPRESENTATION 69 4.4.3 REPRESENTABILITY OF THE GREEN
FUNCTION AND THE WAVE FUNCTION 70 4.4.4 EXAMPLE OF REPRESENTABILITY 73
4.4.5 THE REPRESENTABILITY THEOREM 75 4.5 MUFFIN-TIN POTENTIALS 77
REFERENCES 79 5 MST FOR MUFFIN-TIN POTENTIALS 80 5.1 MULTIPLE SCATTERING
SERIES 81 5.1.1 THE ANGULAR-MOMENTUM REPRESENTATION 83 5.1.2 ELECTRONIC
STRUCTURE OF A PERIODIC SOLID 86 5.2 THE GREEN FUNCTION IN MST 88 5.3
IMPURITIES IN MST 92 5.4 COHERENT POTENTIAL APPROXIMATION 94 5.5
SCREENED MST 96 5.6 ALTERNATIVE DERIVATION OF MST 97 5.7 KORRINGA S
DERIVATION 100 5.8 RELATION TO MUFFIN-TIN ORBITAL THEORY 101 5.9 MST FOR
E 0 102 5.9.1 THE TWO-SCATTERER PROBLEM IN THREE DIMENSIONS . 103 /
CONTENTS XI 5.9.2 ARBITRARY NUMBER OF MT POTENTIALS 107 5.9.3
CONVERGENCE AND ACCURACY OF MST (*) 109 5.10 THE CONVERGENCE PROPERTIES
OF MST (*) ILL 5.10.1 ENERGY CONVERGENCE 112 5.10.2 CONVERGENCE OF THE
WAVE FUNCTION 116 5.10.3 CONVERGENCE OF SINGLE-CENTER EXPANSION OF THE
WAVE FUNCTION 119 5.10.4 SUMMARY 120 REFERENCES 121 6 MST FOR
SPACE-FILLING CELLS 122 6.1 HISTORICAL DEVELOPMENT OF FULL-CELL MST 122
6.2 DERIVATIONS OF MST FOR SPACE-FILLING CELLS 126 6.3 FULL-CELL MST 128
6.3.1 OUTGOING-WAVE BOUNDARY CONDITIONS 130 6.3.2 EMPTY-LATTICE TEST 131
6.3.3 NOTE ON CONVERGENCE 131 6.3.4 FULL-POTENTIAL WAVE FUNCTIONS 133
6.4 THE GREEN FUNCTION AND BLOCH FUNCTION 133 6.4.1 THE GREEN FUNCTION
133 6.4.2 ALTERNATIVE EXPRESSIONS FOR THE GREEN FUNCTION . . 136 6.4.3
BLOCH FUNCTIONS FOR PERIODIC, SPACE-FILLING CELLS . 136 6.5 VARIATIONAL
FORMALISMS 137 6.5.1 VARIATIONAL DERIVATION OF MST 138 6.5.2 A
VARIATIONAL PRINCIPLE FOR MST 138 6.5.3 FIRST VARIATIONAL DERIVATION OF
MST 140 6.6 SECOND VARIATIONAL DERIVATION (*) 146 6.6.1 THE SECULAR
EQUATION FOR NONSPHERICAL MT POTENTIALS 146 6.6.2 SPACE-FILLING CELLS OF
CONVEX SHAPE 149 6.6.3 DISPLACED-CELL APPROACH: CONVEX CELLS (*) 152
6.6.4 DISPLACED-CELL APPROACH: CONCAVE CELLS(*) .... 154 6.7
CONSTRUCTION OF THE WAVE FUNCTION 154 6.8 THE CLOSURE OF INTERNAL SUMS
(*) 156 6.9 NUMERICAL RESULTS 156 6.10 SQUARE VERSUS RECTANGULAR
MATRICES (*) 158 REFERENCES 159 7 AUGMENTED MST(*) 161 7.1 GENERAL
COMMENTS 161 7.2 MST WITH A TRUNCATED BASIS SET: MT POTENTIALS 163 7.3
GENERAL POTENTIALS 164 7.4 GREEN FUNCTIONS AND THE LLOYD FORMULA 169
7.4.1 GREEN FUNCTIONS 169 7.4.2 THE LLOYD FORMULA 171 XII CONTENTS 7.4.3
SINGLE SCATTERER 171 7.4.4 A COLLECTION OF SCATTERERS 174 7.4.5 FIRST
DERIVATION 174 7.4.6 SECOND DERIVATION 176 7.4.7 THE EFFECTS OF
TRUNCATION 178 7.5 NUMERICAL STUDY OF TWO MUFFIN-TIN POTENTIALS 180 7.6
CONVERGENCE OF ELECTRONIC STRUCTURE CALCULATIONS 182 REFERENCES 184 8
RELATIVISTIC FORMALISM 185 8.1 GENERAL COMMENTS 185 8.2 GENERALIZED
PARTIAL WAVES 187 8.2.1 THE FREE-PARTICLE PROPAGATOR IN THE PRESENCE OF
SPIN 189 8.2.2 THE (*, SS) OR * REPRESENTATION 191 8.3 GENERALIZED
STRUCTURE CONSTANTS 193 8.4 FREE-PARTICLE SOLUTIONS 194 8.4.1
FREE-PARTICLE SOLUTION OF THE DIRAC EQUATION . . . . 194 8.4.2 THE
FREE-PARTICLE PROPAGATOR 195 8.5 RELATIVISTIC SINGLE-SITE SCATTERING
THEORY 196 8.5.1 SPHERICALLY SYMMETRIC POTENTIALS 196 8.5.2 SPIN-ORBIT
COUPLING 197 8.5.3 SCALAR RELATIVISTIC EXPRESSIONS 199 8.5.4 GENERALLY
SHAPED, SCALAR POTENTIALS 200 8.6 RELATIVISTIC MULTIPLE SCATTERING
THEORY 202 REFERENCES 202 9 THE POISSON EQUATION 203 9.1 GENERAL
COMMENTS 203 9.2 MULTIPOLE MOMENTS 203 9.3 COMPARISON WITH THE
SCHROEDINGER EQUATION 205 9.4 CONVEX POLYHEDRAL CELLS 207 9.4.1
MATHEMATICAL PRELIMINARIES 207 9.4.2 NON-MT, SPACE-FILLING CELLS OF
CONVEX SHAPE ... 209 9.5 NUMERICAL RESULTS FOR CONVEX CELLS 213 9.6
CONCAVE CELLS 218 9.6.1 ANALYTIC CONTINUATION 218 9.7 DIRECT ANALOGY
WITH MST 220 9.7.1 SINGLE CELL CHARGES 220 9.7.2 MULTIPLE SCATTERING
SOLUTIONS 221 9.7.3 SPACE-FILLING CHARGES OF ARBITRARY SHAPE 222
REFERENCES 225 A TIME-DEPENDENT GREEN FUNCTIONS 226 CONTENTS XIII *
TIME-INDEPENDENT GREEN FUNCTIONS 230 * SPHERICAL FUNCTIONS 231 C.L THE
SPHERICAL HARMONICS 231 C.2 THE BESSEL, NEUMANN, AND HANKEL FUNCTIONS
234 C.3 SOLUTIONS OF THE HELMHOLTZ EQUATION 236 REFERENCES 242 D
DISPLACEMENTS OF SPHERICAL FUNCTIONS 243 REFERENCES 247 E THE
TWO-DIMENSIONAL SQUARE CELL 248 E.L NUMERICAL RESULTS (*) 250 REFERENCES
255 F FORMAL SCATTERING THEORY 256 F.L GENERAL COMMENTS 256 F.2 INITIAL
CONDITIONS AND THE MTFLLER OPERATORS 257 F.3 THE M0LLER WAVE OPERATORS
258 F.4 THE LIPPMANN-SCHWINGER EQUATION 261 REFERENCES 262 G IRREGULAR
SOLUTIONS TO THE SCHROEDINGER EQUATION 264 H DISPLACEMENT OF IRREGULAR
SOLUTIONS 267 I THE INVERSE T-MATRIX AT LARGE L 270 J THE STRUCTURE
CONSTANTS AT LARGE L 272 * CONVERSION OF VOLUME INTEGRALS 274 L ENERGY
DERIVATIVES 275 M CONVERGENCE OF THE SECULAR MATRIX 277 N SUMMARY OF MST
279 N.L GENERAL FRAMEWORK 279 N.2 SINGLE POTENTIAL 280 N.3 MULTIPLE
SCATTERING THEORY 281 INDEX 283
|
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author | Gonis, Antonios Butler, William H. |
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id | DE-604.BV013062798 |
illustrated | Illustrated |
indexdate | 2024-07-09T18:38:29Z |
institution | BVB |
isbn | 038798853X |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008900595 |
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physical | XIII, 285 S. graph. Darst. |
publishDate | 2000 |
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series2 | Graduate texts in contemporary physics |
spelling | Gonis, Antonios Verfasser aut Multiple scattering in solids Antonios Gonis ; William H. Buttler New York [u.a.] Springer 2000 XIII, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in contemporary physics Literaturangaben Diffusion (physique nucléaire) ram Énergie, Bandes d' (physique) ram Energy-band theory of solids Multiple scattering (Physics) Festkörper (DE-588)4016918-2 gnd rswk-swf Vielfachstreuung (DE-588)4188254-4 gnd rswk-swf Elektronenstruktur (DE-588)4129531-6 gnd rswk-swf Vielfachstreuung (DE-588)4188254-4 s Festkörper (DE-588)4016918-2 s Elektronenstruktur (DE-588)4129531-6 s DE-604 Butler, William H. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008900595&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Gonis, Antonios Butler, William H. Multiple scattering in solids Diffusion (physique nucléaire) ram Énergie, Bandes d' (physique) ram Energy-band theory of solids Multiple scattering (Physics) Festkörper (DE-588)4016918-2 gnd Vielfachstreuung (DE-588)4188254-4 gnd Elektronenstruktur (DE-588)4129531-6 gnd |
subject_GND | (DE-588)4016918-2 (DE-588)4188254-4 (DE-588)4129531-6 |
title | Multiple scattering in solids |
title_auth | Multiple scattering in solids |
title_exact_search | Multiple scattering in solids |
title_full | Multiple scattering in solids Antonios Gonis ; William H. Buttler |
title_fullStr | Multiple scattering in solids Antonios Gonis ; William H. Buttler |
title_full_unstemmed | Multiple scattering in solids Antonios Gonis ; William H. Buttler |
title_short | Multiple scattering in solids |
title_sort | multiple scattering in solids |
topic | Diffusion (physique nucléaire) ram Énergie, Bandes d' (physique) ram Energy-band theory of solids Multiple scattering (Physics) Festkörper (DE-588)4016918-2 gnd Vielfachstreuung (DE-588)4188254-4 gnd Elektronenstruktur (DE-588)4129531-6 gnd |
topic_facet | Diffusion (physique nucléaire) Énergie, Bandes d' (physique) Energy-band theory of solids Multiple scattering (Physics) Festkörper Vielfachstreuung Elektronenstruktur |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008900595&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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