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Theory of single and multiple interfaces Book

Theory of single and multiple interfaces
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  • Theory of single and multiple interfaces
  • Written by author F. Garcia-Moliner
  • Published by Singapore ; World Scientific, c1992., 7/1/1992
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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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