Semiclassical description of resonant tunneling

We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The tunneling current is measured at the second interface of this well and our calculations idealized an experimental situation where a strong magnetic field tilted with respect to an electric field was used. It is shown that the contribution to the tunneling current, due to trajectories which begin at the first interface and end on the second, is dominant for special periodic orbits which hit both walls of the quantum well and are perpendicular to the first wall. The resulting formula, which is a semiclassical expression for the total tunneling current, differs in a few important aspects from the Gutzwiller trace formula for the density of states. The Miller-type modification of the obtained semiclassical formula for stable orbits is also discussed.