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Book Categories |
Preface | ||
1 | Technical Preliminaries | 1 |
1.1 | Generalities on Green Functions and Related Concepts | 1 |
1.2 | Continuous and Discrete Systems | 5 |
1.3 | Continuous Systems: Description of the Bulk in Terms of Planar Projections | 12 |
1.4 | Discrete Systems: Layer Description of the Bulk | 23 |
2 | General Form of the SGFM Method | 29 |
2.1 | A Reminder of Scattering Theory | 29 |
2.2 | Scattering and Matching: The General SGFM Formulae | 32 |
2.3 | Planar Geometry: Continuous Media | 37 |
2.4 | Planar Geometry: Discrete Media | 45 |
2.5 | Amplitude Transfer Matrix, Wavefunction Normalisation and Density of States | 50 |
3 | Matching Analysis for Continuous Systems | 55 |
3.1 | Continuity Conditions for Planar Projections | 55 |
3.2 | Discontinuity Conditions, Matching Rules and the Matching Formula | 62 |
3.3 | Some Practical Examples | 66 |
3.4 | The Wavefunction and the Logarithmic Derivatives | 82 |
3.5 | Physical Meaning of the Matching Secular Equation | 85 |
3.6 | A Theorem on Arbitrary Extended Pseudomedia | 89 |
4 | Matching for a Discrete System | 95 |
4.1 | The Meaning of Matching for Discrete Crystals | 95 |
4.2 | The Matching Formula for Discrete Interfaces | 97 |
4.3 | The Free Surface: Examples | 104 |
5 | SGFM For Coupled Interfaces | 119 |
5.1 | Two Plane Interfaces. Continuous Media | 119 |
5.2 | Study of the Superlattice. Continuous Media | 135 |
5.3 | Examples of Layered Continuous Systems | 144 |
5.4 | Coupled Interfaces. Discrete Media | 166 |
5.5 | Examples of Superperiodic Discrete Systems | 179 |
5.6 | Structural Green Function and Truncated Superlattices | 189 |
6 | The Geometry of the Matching Surface | 205 |
6.1 | Matching on a Sphere or a Cylinder | 205 |
6.2 | A Three-dimensional Lattice of Sphere: SGFM Study of a Muffin Tin Crystal | 217 |
6.3 | A Two-dimensional Lattice of Cylinders or Disks | 230 |
6.4 | A Sphere and a Plan or Two Spheres | 241 |
7 | The Full Transfer Matrix and SGFM For Continuous Media | 249 |
7.1 | The Full Transfer Matrix and the Scalar Green Function | 249 |
7.2 | Scalar SGFM from the Full Transfer Matrices | 263 |
7.3 | General Analysis of the Matrix Case | 269 |
7.4 | Finding the Green Function for an Arbitrary Medium | 276 |
7.5 | Matrix SGFM from the Full Transfer Matrices | 283 |
7.6 | Wavefunction, Green Function and Transfer Matrices for a General System | 291 |
7.7 | Evaluation of the Full Transfer Matrix | 295 |
7.8 | Some Practical Examples | 299 |
8 | Transfer Matrix and SGFM For Discrete Media | 323 |
8.1 | Transfer Matrices for Discrete Crystalline Media | 323 |
8.2 | SGFM from the Transfer Matrices | 330 |
8.3 | Some Practical Examples | 336 |
9 | A Miscellany of Problems Related to Matching | 369 |
9.1 | Selfconsistent Matching Calculations | 370 |
9.2 | Disordered Interfaces | 372 |
9.3 | Long Wave Surface Spin Waves | 381 |
9.4 | Problems Involving Coupled Fields: Piezoelectric and Magnetoelastic Surface Waves | 391 |
9.5 | Longitudinal and Transverse Fields in Matched Systems | 405 |
9.6 | Matching with Discontinuities | 421 |
9.7 | Surface Waves in Fluids | 428 |
A: Matching with Envelope Function Model Hamiltonians | 439 | |
References | 472 | |
References | 473 | |
Index | 495 |
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