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Journal of Mathematical Chemistry

Average energy and quantum similarity of a time dependent quantum system subject to Pöschl–Teller potential

Ramon Carbó‐Dorca, Debraj Nath

Published Jan 10, 2022• 5 citations
Publisher
DOI
10.1007/s10910-021-01318-3

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We study the scattering of a Gaussian wave packet in the modified Pöschl–Teller potential well in time respect. Analytical expressions of average dwell time, phase time, and average traversal time due to Larmor-clock times are obtained, from which the average traversal time can be identified with the average dwell time. We observe that the average dwell time is appreciably longer than the phase time at low energies, but they tend to coincide in the limit of narrow momentum distribution, high energy, and large interaction region. We also find that both of them are longer than the classical scattering time in the potential. All of these times are, however, shorter than the free-particle time, demonstrating the acceleration effect of the potential in temporal aspect of the scattering.