Wave Propagation in Linear Media | re-examined

More documents

Recommendations

Info

4 One-dimensional quantum tunnelling 72 4.1 The potential step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.2 Initial wave forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3 Examples of scattering processes . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4 The square barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.5 Tunnelling time de nitions for a square barrier . . . . . . . . . . . . . . . . . 96 4.6 Examples of tunnelling events . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Interlude Wave functions in graphical representation 119 Part II Numerical aspects of wave equations 123 5 Numerical quadrature and extrapolation 124 5.1 Univariate numerical quadrature . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.1.1 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.1.2 Computer routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2 Convergence acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6 Towards a quadrature routine 132 6.1 Partitioning the integration interval . . . . . . . . . . . . . . . . . . . . . . . 133 6.2 Choosing the rst partition point . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.3 How to compute the rst integral . . . . . . . . . . . . . . . . . . . . . . . . . 141 6.4 Asymptotic partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.5 Considerations for a Mathematica implementation . . . . . . . . . . . . . . . 149 6.6 Controlling the accuracy of the extrapolation result . . . . . . . . . . . . . . . 155 7 Mathematica implementation of a quadrature function 161 7.1 User interface of the function OscInt . . . . . . . . . . . . . . . . . . . . . . . 161 7.2 Structure of the package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.3 Implementation of OscInt and related functions . . . . . . . . . . . . . . . . 165 7.3.1 OscInt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.3.2 PartitionTable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 7.3.3 PartitionOffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 XIV
7.3.4 PartitionPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 7.3.5 PartInt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 7.3.6 OscIntControlled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 7.4 Auxiliary functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 7.4.1 Zero computation for quadratic arguments . . . . . . . . . . . . . . . . 174 7.4.2 Zero computation for hyperbolic arguments . . . . . . . . . . . . . . . 174 7.4.3 Approximation error control . . . . . . . . . . . . . . . . . . . . . . . . 178 7.5 Test of the quadrature routine . . . . . . . . . . . . . . . . . . . . . . . . . . 181 8 Application of the quadrature routine 190 8.1 Preparation of the wave integrals for quadrature . . . . . . . . . . . . . . . . 191 8.2 Outline of the program structure . . . . . . . . . . . . . . . . . . . . . . . . . 197 8.3 Implementation of the quadrature modules . . . . . . . . . . . . . . . . . . . 200 8.4 Test of the package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 8.4.1 Numerical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 8.4.2 Formal veri cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 A Mathematica packages 214 A.1 Numerical quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 A.2 Solutions for the step potential . . . . . . . . . . . . . . . . . . . . . . . . . . 221 A.3 Solutions for the square barrier . . . . . . . . . . . . . . . . . . . . . . . . . . 229 A.4 Electromagnetic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 A.5 Utilities for displaying points in 3D . . . . . . . . . . . . . . . . . . . . . . . . 234 Bibliography 237 Index 247 XV
Page 1 and 2: DISSERTATION Wave Propagation in Li
Page 3: Kurzfassung Seit der Entdeckung des
Page 7 and 8: Nullum est iam dictum, quod non sit
Page 9 and 10: Preface Our popular writers and rep
Page 11 and 12: the quest for superluminality and t
Page 13: Contents Part I Wave propagation ph
Page 17 and 18: Part I Wave propagation phenomena S
Page 19 and 20: 1.1 Phase and group velocity 1.1 Ph
Page 21 and 22: 1.1 Phase and group velocity ! !c v
Page 23 and 24: 1.2 A few notes on dispersion He co
Page 25 and 26: 1.2 A few notes on dispersion v/c 6
Page 27 and 28: 1.3 Signal velocity dipoles with a
Page 29 and 30: 1.3 Signal velocity The arbitrarine
Page 31 and 32: 1.4 Energy velocity For electromagn
Page 33 and 34: 1.5 Other velocity de nitions For n
Page 35 and 36: 1.5 Other velocity de nitions evide
Page 37 and 38: 2.1 Superluminal wave propagation 2
Page 39 and 40: 2.1 Superluminal wave propagation a
Page 41 and 42: 2.1 Superluminal wave propagation t
Page 43 and 44: 2.2 Quantum mechanical tunnelling e
Page 45 and 46: 2.2 Quantum mechanical tunnelling R
Page 47 and 48: Chapter 3 Wave propagation in elect
Page 49 and 50: 3.1 Model of a transmission line th
Page 51 and 52: 3.2 Excursion: a delay line section
Page 53 and 54: 3.3 Re ection due to termination mi
Page 55 and 56: 3.4 A simple thought experiment I0
Page 57 and 58: 3.5 A dispersive system: the lossle
Page 63 and 64: 3.6 Inhomogeneous transmission line
Page 65 and 66:
3.7 Turn-on e ects in a lossless pl
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
3.8 Turn-on e ects in a wave guide
Page 79 and 80:
3.8 Turn-on e ects in a wave guide
Page 81 and 82:
3.9 A Gaussian pulse in plasma Like
Page 83 and 84:
3.9 A Gaussian pulse in plasma 250
Page 85 and 86:
3.9 A Gaussian pulse in plasma 250
Page 87 and 88:
3.9 A Gaussian pulse in plasma Note
Page 89 and 90:
4.1 The potential step 4.1 The pote
Page 91 and 92:
4.1 The potential step Inside the b
Page 93 and 94:
4.2 Initial wave forms -60 -50 -40
Page 95 and 96:
4.2 Initial wave forms -60 -50 -40
Page 97 and 98:
4.3 Examples of scattering processe
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
4.4 The square barrier they have va
Page 111 and 112:
4.4 The square barrier 1 0.8 0.6 0.
Page 113 and 114:
4.5 Tunnelling time de nitions for
Page 115 and 116:
4.5 Tunnelling time de nitions for
Page 117 and 118:
4.6 Examples of tunnelling events P
Page 119 and 120:
4.6 Examples of tunnelling events 2
Page 121 and 122:
4.6 Examples of tunnelling events -
Page 123 and 124:
4.6 Examples of tunnelling events t
Page 125 and 126:
4.6 Examples of tunnelling events P
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
4.6 Examples of tunnelling events T
Page 135 and 136:
Interlude Wave functions in graphic
Page 137 and 138:
Wave functions in graphical represe
Page 139 and 140:
Part II Numerical aspects of wave e
Page 141 and 142:
5.1 Univariate numerical quadrature
Page 143 and 144:
5.1 Univariate numerical quadrature
Page 145 and 146:
5.2 Convergence acceleration one, t
Page 147 and 148:
5.2 Convergence acceleration (1) ,1
Page 149 and 150:
6.1 Partitioning the integration in
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
6.2 Choosing the rst partition poin
Page 157 and 158:
6.3 How to compute the rst integral
Page 159 and 160:
6.3 How to compute the rst integral
Page 161 and 162:
6.4 Asymptotic partition consuming
Page 163 and 164:
6.4 Asymptotic partition of the int
Page 165 and 166:
6.5 Considerations for a Mathematic
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
6.6 Controlling the accuracy of the
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Chapter 7 Mathematica implementatio
Page 179 and 180:
7.1 User interface of the function
Page 181 and 182:
7.3 Implementation of OscInt and re
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
7.4 Auxiliary functions While[itera
Page 191 and 192:
7.4 Auxiliary functions Linear appr
Page 193 and 194:
7.4 Auxiliary functions For the sak
Page 195 and 196:
7.4 Auxiliary functions Out[8]= 3 f
Page 197 and 198:
7.5 Test of the quadrature routine
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
8.1 Preparation of the wave integra
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
8.2 Outline of the program structur
Page 215 and 216:
8.2 Outline of the program structur
Page 217 and 218:
8.3 Implementation of the quadratur
Page 219 and 220:
8.3 Implementation of the quadratur
Page 221 and 222:
8.4 Test of the package 8.4 Test of
Page 223 and 224:
8.4 Test of the package -200 -150 -
Page 225 and 226:
8.4 Test of the package 0.4 0.2 -0.
Page 227 and 228:
8.4 Test of the package 8.4.2 Forma
Page 229 and 230:
8.4 Test of the package Out[24]= 0
Page 231 and 232:
A.1 Numerical quadrature Asymptotic
Page 233 and 234:
A.1 Numerical quadrature WynnDegree
Page 235 and 236:
A.1 Numerical quadrature Which[ft =
Page 237 and 238:
A.2 Solutions for the step potentia
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
A.3 Solutions for the square barrie
Page 247 and 248:
A.3 Solutions for the square barrie
Page 249 and 250:
A.4 Electromagnetic waves function
Page 251 and 252:
A.5 Utilities for displaying points
Page 253 and 254:
Bibliography Bibliography [1] James
Page 255 and 256:
Bibliography [29] Kurt Edmund Oughs
Page 257 and 258:
Bibliography [59] Ch. Spielmann, R.
Page 259 and 260:
Bibliography [91] C. R. Leavens and
Page 261 and 262:
Bibliography [123] T. O. Espelid an
Page 263 and 264:
Index Index absorption, 7, 9 accura
Page 265 and 266:
Index saddle point integration, 11,
Page 267:
Curriculum vitae Dipl.-Ing. Thilo S
show all

Wave Propagation in Linear Media | re-examined

Create successful ePaper yourself

Delete template?

Save as template?