Vectorlike representation of one-dimensional scattering

Details Vectorlike representation of one-dimensional scattering Vectorlike representation of one-dimensional scattering

2004-11-11

arxiv.org/abs/quant-ph/0411081v1

European Journal of Physics 26, 469 (2005)

Physics

Quantum Physics

8 pages, 5 figures. This paper is dedicated to Alberto Galindo the occasion of his seventieth birthday. Submitted for publicat

Scientific paper

We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By generalizing to the unit disk the idea of turns, introduced by Hamilton to represent rotations on the sphere, we develop a method to represent transfer matrices by hyperbolic turns, which can be composed by a simple parallelogramlike rule.

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