  A quantum wire of uniform cross section (but with eventual disorder) with
three regions: dot, left lead, and right lead, is considered. Assuming that the
same unitary transformation diagonalizes all unit cells of this wire, we
propose a new formula for the calculation of the Greens function (GF) and the
coherent transmission coefficient. This formula allows to calculate these
quantitites much faster than the standard methods. In particular, the problem
of a uniform dot (simple cubic uniform dot attached to the simple cubic wire),
with all onsites equal and all hoppings equal is solved fully analytically. The
energy and dot-length dependence of the GF, local density of states (LDOS), the
transmission coefficient and bound state energies are also derived.
