Wave Propagation in Linear Media | re-examined

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Bibliography [107] Abraham Goldberg, Harry M. Schey, and Judah L. Schwartz. Computer-Generated Motion Pictures of One-Dimensional Quantum-Mechanical Transmission and Re ection Phenomena. American Journal of Physics, 35(3):177{186, 1967. [108] S. Collins, David Lowe, and J. R. Barker. A dynamic analysis of resonant tunnelling. J. Phys. C: Solid State Phys., 20:6233{6243, 1987. [109] Terry Robb. Schroedinger's Equation. Mathematica notebook available on MathSource, 1994. URL:http://www.mathsource.com/cgi-bin/MathSource/Enhancements/ Interfacing/InterCall/0204-657. [110] John R. Hiller, Ian D. Johnston, and Daniel F. Styer. Quantum Mechanics Simulations, The Consortium for Upper-Level Physics Software. John Wiley & Sons, New York, 1995. [111] John R. Merrill. Waves in Dispersive Media: Another Use of Computers in Introductory Physics. American Journal of Physics, 39:539{544, 1971. [112] Milton Abramowitz. On the Practical Evaluation of Integrals. SIAM Journal of Applied Mathematics, 2:20{35, 1954. [113] Philip J. Davis and Philip Rabinowitz. Methods of numerical integration. Academic Press, Inc., Orlando, Florida, second edition, 1984. [114] David Levin. Procedures for computing one and two dimensional integrals of functions with rapid irregular oscillations. Mathematics of Computation, 38(158):531{538, 1982. [115] G. A. Evans. Two robust methods for irregular oscillatory integrals over a nite range. Applied Numerical Mathematics, 14(4):383{395, 1994. [116] L. N. G. Filon. On a quadrature formula for trigonometric integrals. Proc. Roy. Soc. Edinburgh, 49:38{47, 1928. [117] Ulf Torsten Ehrenmark. A three-point formula for numerical quadrature of oscillatory integrands with variable frequency. Journal of Computational and Applied Mathematics, 21:87{99, 1988. [118] Pei-Cheng Xu and A. K. Mal. An adaptive integration scheme for irregularly oscillatory functions. Wave Motion, 7:235{243, 1985. [119] K. T. R. Davies. Complex-plane methods for evaluating integrals with highly oscillatory integrands. Journal of Computational Physics, 80(2):498{505, 1989. [120] Philip Rabinowitz. Extrapolation methods in numerical integration. Numerical Algorithms, 3:17{28, 1992. [121] J. N. Lyness. Integrating some in nite oscillating tails. Journal of Computational and Applied Mathematics, 12 & 13:109{117, 1985. [122] James Lyness and Gwendolen Hines. To Integrate Some In nite Oscillating Tails. ACM Transactions on Mathematical Software, 12(1):24{25, 1986. 244
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Page 1 and 2:
DISSERTATION Wave Propagation in Li
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Kurzfassung Seit der Entdeckung des
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Nullum est iam dictum, quod non sit
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Preface Our popular writers and rep
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the quest for superluminality and t
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Contents Part I Wave propagation ph
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7.3.4 PartitionPoints . . . . . . .
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Part I Wave propagation phenomena S
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1.1 Phase and group velocity 1.1 Ph
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1.1 Phase and group velocity ! !c v
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1.2 A few notes on dispersion He co
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1.2 A few notes on dispersion v/c 6
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1.3 Signal velocity dipoles with a
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1.3 Signal velocity The arbitrarine
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1.4 Energy velocity For electromagn
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1.5 Other velocity de nitions For n
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1.5 Other velocity de nitions evide
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2.1 Superluminal wave propagation 2
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2.1 Superluminal wave propagation a
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2.1 Superluminal wave propagation t
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2.2 Quantum mechanical tunnelling e
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2.2 Quantum mechanical tunnelling R
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Chapter 3 Wave propagation in elect
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3.1 Model of a transmission line th
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3.2 Excursion: a delay line section
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3.3 Re ection due to termination mi
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3.4 A simple thought experiment I0
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3.5 A dispersive system: the lossle
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3.6 Inhomogeneous transmission line
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3.7 Turn-on e ects in a lossless pl
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3.8 Turn-on e ects in a wave guide
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3.8 Turn-on e ects in a wave guide
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3.9 A Gaussian pulse in plasma Like
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3.9 A Gaussian pulse in plasma 250
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3.9 A Gaussian pulse in plasma 250
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3.9 A Gaussian pulse in plasma Note
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4.1 The potential step 4.1 The pote
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4.1 The potential step Inside the b
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4.2 Initial wave forms -60 -50 -40
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4.2 Initial wave forms -60 -50 -40
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4.3 Examples of scattering processe
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4.4 The square barrier they have va
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4.4 The square barrier 1 0.8 0.6 0.
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4.5 Tunnelling time de nitions for
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4.5 Tunnelling time de nitions for
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4.6 Examples of tunnelling events P
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4.6 Examples of tunnelling events 2
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4.6 Examples of tunnelling events -
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4.6 Examples of tunnelling events t
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4.6 Examples of tunnelling events P
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4.6 Examples of tunnelling events T
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Interlude Wave functions in graphic
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Wave functions in graphical represe
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Part II Numerical aspects of wave e
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5.1 Univariate numerical quadrature
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5.1 Univariate numerical quadrature
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5.2 Convergence acceleration one, t
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5.2 Convergence acceleration (1) ,1
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6.1 Partitioning the integration in
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6.2 Choosing the rst partition poin
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6.3 How to compute the rst integral
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6.3 How to compute the rst integral
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6.4 Asymptotic partition consuming
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6.4 Asymptotic partition of the int
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6.5 Considerations for a Mathematic
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6.6 Controlling the accuracy of the
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Chapter 7 Mathematica implementatio
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7.1 User interface of the function
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7.3 Implementation of OscInt and re
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7.4 Auxiliary functions While[itera
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7.4 Auxiliary functions Linear appr
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7.4 Auxiliary functions For the sak
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7.4 Auxiliary functions Out[8]= 3 f
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7.5 Test of the quadrature routine
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8.1 Preparation of the wave integra
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Page 213 and 214: 8.2 Outline of the program structur
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Page 217 and 218: 8.3 Implementation of the quadratur
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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 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: Bibliography [91] C. R. Leavens and
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
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