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 Gp(t) and |Ψ(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.

Generic short-time propagation of sharp-boundaries wave packets

“…Recently, the shutter problem was recruited by many researchers in studies of fundamental issues in Quantum Mechanics, like the passage-time in tunneling [8], particle absorption and imaginary potential [9] and quantum measurements and collapse [10].…”

Low Temperature Plasma Enhanced Chemical Vapor Deposition-Synthesized Electrochromic MoOxCy Thin Films for Flexible Electrochromic Devices

“…Our calculation extends the results of the shutter problem, where the initial plane wave occupied the space axis at one side of the barrier and was specially suited to study the propagation of the wave front and the tunnelling time [3,4].…”

Role of top and under-the-barrier complex transmission poles for the delay time in single barrier tunneling

“…The M functions are defined in terms of the complex error function [11,12] w͑z͒ = exp͑−z 2 ͒erfc͑−iz͒, as M͑y q ͒ = exp͓imx 2 /2បt͔w͑iy q ͒ /2, where y q = e −i/4 ͑m /2បt͒ 1/2 ͓x − បqt / m͔, and q = ±k, k ±n . An alternative representation for ⌿ e ͑x , t͒ has been recently obtained by using a plane-wave expansion of the timedependent wave function [13]. It reads ⌿ e ͑x,t͒ = ik…”