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

Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the “passage time” in tunneling