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Quantum Transport in Mesoscopic SystemsComplexity and Statistical Fluctuations. A Maximum Entropy Viewpoint$
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Pier A. Mello and Narendra Kumar

Print publication date: 2004

Print ISBN-13: 9780198525820

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525820.001.0001

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INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY I: ONE-DIMENSIONAL SCATTERING

INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY I: ONE-DIMENSIONAL SCATTERING

Chapter:
(p.15) 2 INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY I: ONE-DIMENSIONAL SCATTERING
Source:
Quantum Transport in Mesoscopic Systems
Author(s):

Pier A. Mello

Narendra Kumar

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525820.003.0002

This chapter is devoted to basic potential scattering theory, focusing on the case of a one-dimensional conductor and an open cavity with a one-channel lead connected to it. The contents of this chapter include potential scattering in infinite one-dimensional space; Lippmann-Schwinger equation; free Green function; reflection and transmission amplitudes; transfer matrix; T matrix; S matrix and its analytic structure; phase shifts and resonances from the analytic structure of S matrix in complex momentum and complex energy planes; parametrization of the matrices; combination of the S matrices for two scatterers in series; and invariant-imbedding approach for a one-dimensional disordered conductor.

Keywords:   scattering matrix, transfer matrix, R-matrix theory, Poisson kernel, ergodicity, Green function, Lippmann-Schwinger equation, reflection amplitude, transmission amplitude, invariant imbedding

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