Transmission time of a particle in the reflectionless Sech-squared potential: Quantum clock approach

We investigate the time for a particle to pass through the reflectionless Sech-squared potential. Using the Salecker-Wigner and Peres quantum clock an average transmission time of a Gaussian wave packet representing the particle is explicitly evaluated in terms of average momentum and travel distance. The average transmission time is shown to be shorter than the time of free-particle motion and very close to the classical time for wave packets with well-localized momentum states. Since the clock measures the duration of scattering process the average transmission time can be interpreted as the average dwell time.