Exact vs. quasi-classical tunneling times for idealized potentials

We compare the exact tunneling time with the quasi-classical tunneling time for idealized potentials. We examine three one-dimensional cases where the potential is chosen to have a simple form. In each case, the exact tunneling time and the quasiclassical time differ significantly. In one case, the two differ in magnitude by a factor of about ten. In another case, the two differ not only quantitatively, but qualitatively as well. A discussion is given as to why the two times are significantly different, and suggestions for further inquiries are made.