# A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics

@article{Mostafazadeh2014ADF, title={A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics}, author={Ali Mostafazadeh}, journal={Annals of Physics}, year={2014}, volume={341}, pages={77-85} }

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…

## 34 Citations

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The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the $S$-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that…

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