Chapter

INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY II: SCATTERING INSIDE WAVEGUIDES AND CAVITIES

Pier A. Mello and Narendra Kumar

in Quantum Transport in Mesoscopic Systems

Published in print May 2004 | ISBN: 9780198525820
Published online September 2007 | e-ISBN: 9780191712234 | DOI: https://dx.doi.org/10.1093/acprof:oso/9780198525820.003.0003

Series: Mesoscopic Physics and Nanotechnology

 INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY II: SCATTERING INSIDE WAVEGUIDES AND CAVITIES

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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.

Keywords: Lippmann-Schwinger equation; scattering matrix; transfer matrix; Wigner R-matrix; time-reversal invariance; open channel; close channel

Chapter.  37265 words.  Illustrated.

Subjects: Condensed Matter Physics

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