
Published online:
01 September 2007
Published in print:
20 May 2004
Online ISBN:
9780191712234
Print ISBN:
9780198525820
Contents
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3.1 Quasi-one-dimensional scattering theory 3.1 Quasi-one-dimensional scattering theory
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3. 1.1 The reflection and transmission amplitudes; the Lippmann–Schwinger coupled equations 3. 1.1 The reflection and transmission amplitudes; the Lippmann–Schwinger coupled equations
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3.1.2 The S matrix 3.1.2 The S matrix
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3.1.3 The transfer matrix 3.1.3 The transfer matrix
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3.1.4 Combining the S matrices for two scatterers in series 3.1.4 Combining the S matrices for two scatterers in series
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3.1.5 Transformation of the scattering and transfer matrices under a translation 3.1.5 Transformation of the scattering and transfer matrices under a translation
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3.1.6 Exactly soluble example for the two-channel problem Two open channels 3.1.6 Exactly soluble example for the two-channel problem Two open channels
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3.1.7 Extension of the S and M matrices to include open and closed channels 3.1.7 Extension of the S and M matrices to include open and closed channels
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3.2 Scattering by a cavity with an arbitrary number of waveguides 3.2 Scattering by a cavity with an arbitrary number of waveguides
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3.2.1 Statement of the problem 3.2.1 Statement of the problem
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3.2.2 The S matrix; the reflection and transmission amplitudes 3.2.2 The S matrix; the reflection and transmission amplitudes
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3.3 The R-matrix theory of two-dimensional scattering 3.3 The R-matrix theory of two-dimensional scattering
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Chapter
3 INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY II: SCATTERING INSIDE WAVEGUIDES AND CAVITIES
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Pages
120–186
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Published:May 2004
Cite
Mello, Pier A., and Narendra Kumar, 'INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY II: SCATTERING INSIDE WAVEGUIDES AND CAVITIES', Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint, Mesoscopic Physics and Nanotechnology (Oxford , 2004; online edn, Oxford Academic, 1 Sept. 2007), https://doi.org/10.1093/acprof:oso/9780198525820.003.0003, accessed 16 May 2025.
Abstract
This chapter extends the potential scattering theory developed in Chapter 2 to a relatively advanced level with emphasis on quasi-one-dimensional (multi-channel) systems, the associated scattering and transfer matrices, and on how to combine them serially. Both the closed and the open channels are discussed. Scattering by a cavity with an arbitrary number of waveguides (the leads) attached to it is introduced. The Wigner R-matrix theory of two-dimensional scattering is treated in some detail with attention to boundary conditions. A non-trivial exactly soluble example for the two-channel scattering problem is also presented.
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