  Using canonical transformations we diagonalize approximately the Hamiltonian
of a gaussian wire with Rashba spin-orbit interaction. This proceedure allows
us to obtain the energy dispersion relations and the wavefunctions with good
accuracy, even in systems with relatively strong Rashba coupling. With these
eigenstates one can calculate the non-equilibrium spin densities induced by
applying bias voltages across the sample. We focus on the $z$-component of the
spin density, which is related to the spin Hall effect.
