SEMICLASSICAL TUNNELING THROUGH OPAQUE BARRIERS, EXTERNAL INTERACTIONS AND THE TRAVERSAL TIME WAVE-FUNCTION

We show how semiclassical scattering (tunneling) can be analysed in te rms of traversal times. Real or complex valued saddle points are assoc iated with the traversal time wavefunction and they determine the semi classical traversal times. For free particle motion, there is a real s addle point located at the classical traversal time, tau(O). For tunne ling through an opaque rectangular barrier, the saddle point lies at - i tau(BL,) where tau(BL) is the Buttiker-Landauer time. As a result, a lthough physically significant, tau(BL) does not have the physical int erpretation as the actual duration for tunneling. Rather, tau(BL) prov ides an estimate for the range of traversal times of those Feynman pat hs which contribute significantly to the tunneling. We also find the c omplex semiclassical traversal times and transmission probabilities fo r tunneling in the presence of absorption and for interaction with a s low oscillatory mode.