2019/08/31 by Dean Alvin L. Pablico, Eric A. Galapon
Chemistry · Computer Science · Physics and Astronomy · #Algorithm #Chemistry #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Network packet #Operator (biology) #Physics #Quantization (signal processing) #Quantum #Quantum Information and Cryptography #Quantum mechanics #Quantum optics and atomic interactions #Tree traversal #Wave packet #quant-ph
paper · pdf · doi:10.1103/physreva.101.022103
published as Phys. Rev. A 101, 022103 (2020)
arxiv created 2019/11/14 · openalex publication_date 2020/02/10 · arxiv updated 2020/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the quantum traversal time of an incident wave packet across a potential well using the theory of quantum time of arrival (TOA) operators. This is done by constructing the corresponding TOA operator across a potential well via quantization. The expectation value of the potential-well TOA operator is compared to the free-particle case for the same incident wave packet. The comparison yields a closed-form expression of the quantum well traversal time which explicitly shows the classical contributions of the positive and negative momentum components of the incident wave packet and a purely quantum-mechanical contribution significantly dependent on the well depth. An incident Gaussian wave packet is then used as an example. It is shown that for shallow potential wells, the quantum well traversal time approaches the classical traversal time across the well region when the incident wave packet is spatially broad and approaches the expected quantum free-particle traversal time when the wave packet is localized. For deep potential wells, the quantum traversal time oscillates from positive to negative, implying that the wave packet can be advanced or delayed.