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In this paper the transmittance through a quantum wire connected with twoelectron reservoirs is calculated and non-trivial transformation between theevolution operator method and the Green's function technique is reported. Toshow this equivalence an analytical nonlinear formula which concernssymmetrical tridiagonal matrices is proofed. This formula connects the cofactorand three determinants of tridiagonal matrices.

Useful equation of tridiagonal matrices in application to electron transport through a quantum wire