Scattering states for a finite chain in one dimension

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Abstract
Using the transfer matrix method, the solution of the scattering problem on the finite periodic chain of equal symmetric potentials is found in terms of the partial reflection and transmission coefficients. A simple algebraic result is presented showing that the transmission coefficient oscillates rapidly between one and some lower value when the energies lie in the allowed Bloch band. A special case of delta potentials is discussed using the momentum representation. The explicit form for the transmission amplitude can also be used to determine positions of the bound states.

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