  Electron transport properties in nanostructures can be modeled, for example,
by using the semiclassical Wigner formalism or the quantum mechanical Green's
functions formalism. We compare the performance and the results of these
methods in the case of magnetic resonant-tunneling diodes. We have implemented
the two methods within the self-consistent spin-density-functional theory. Our
numerical implementation of the Wigner formalism is based on the
finite-difference scheme whereas for the Green's function formalism the
finite-element method is used. As a specific application, we consider the
device studied by Slobodskyy et all. [Phys. Rev. Lett. 90, 246601 (2003)] and
analyze their experimental results. The Wigner and Green's functions formalisms
give similar electron densities and potentials but, surprisingly, the former
method requires much more computer resources in order to obtain numerically
accurate results for currents. Both of the formalisms can successfully be used
to model magnetic resonant tunneling diode structures.
