Equivalence between the real time Feynman histories and the quantum shutter approaches for the "passage time" in tunneling

Abstract

We show the equivalence of the functions $G_{\mathrm{p}}(t)$ and $|\Psi (d,t){|}^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using the Gell-Mann and Hartle's decoherence functional, and the latter involving an exact analytical solution to the time-dependent Schrödinger equation for cutoff initial waves.