Useful equation of tridiagonal matrices in application to electron transport through a quantum wire
Abstract
In this paper the transmittance through a quantum wire connected with two electron reservoirs is calculated and non-trivial transformation between the evolution operator method and the Green's function technique is reported. To show this equivalence an analytical nonlinear formula which concerns symmetrical tridiagonal matrices is proofed. This formula connects the cofactor and three determinants of tridiagonal matrices.
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