An approach to inverse scattering problems for discrete Schrödinger equations, which are discrete three‐term recursions, is presented by systematically transforming them into discrete two‐component wave‐propagation equations. The wave‐propagation equations permit the immediate application of certain computationally efficient and physically insightful ‘‘layer‐peeling’’ algorithms for inverse scattering. The mapping of three‐term recursions to two‐component evolution equations is one to many, because the relation between the ‘‘potential’’ sequence parametrizing Schrödinger equations and the ‘‘reflection coefficient’’ sequence determining local wave interaction is a nonlinear difference equation. This mapping is examined in some detail and it is used to study both direct and inverse scattering problems associated with discrete Schrödinger equations.

Topics
Wave mechanics, Wave propagation, Partial differential equations, Recurrence relations, Inverse scattering, Scattering problem, Schrodinger equations
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© 1987 American Institute of Physics.
1987
American Institute of Physics
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