Quantum tunneling properties from a Wigner function study

We use a Wigner function description of a Gaussian wave packet to study tunneling through single and double quantum barriers. We note a tunneling time proportional to 1/k and a constant delay time associated with tunneling for the single barrier. The resonant structure gives rise to peaks in tunneling time associated with the resonant energy of the system. We study the initial distribution for the resonant tunneling diode. This is computed from a scattering state basis. Time evolution of the resonant tunneling system is then performed, yielding transient and steady-state results for the I-V curves.