Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dynamical Formulation of One-Dimensional Scattering Theory and Its
  Applications in Optics   We develop a dynamical formulation of one-dimensional scattering theory where
the reflection and transmission amplitudes for a general, possibly complex and
energy-dependent, scattering potential are given as solutions of a set of
dynamical equations. By decoupling and partially integrating these equations,
we reduce the scattering problem to a second order linear differential equation
with universal initial conditions that is equivalent to an initial-value
time-independent Schrodinger equation. We give explicit formulas for the
reflection and transmission amplitudes in terms of the solution of either of
these equations and employ them to outline an inverse-scattering method for
constructing finite-range potentials with desirable scattering properties at
any prescribed wavelength. In particular, we construct optical potentials
displaying threshold lasing, anti-lasing, and unidirectional invisibility.

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The categories of this paper are: cs
37
The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg