Department of Mathematics2024-11-0920140003-491610.1016/j.aop.2013.11.0082-s2.0-84889675454http://dx.doi.org/10.1016/j.aop.2013.11.008https://hdl.handle.net/20.500.14288/14161We 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, antilasing, and unidirectional invisibility.PhysicsJournal Article1096-035X329557500005Q25489