2022/03/08 by X. Gutiérrez de la Cal, M. Pons, D. Sokolovski
Mathematics · Physics and Astronomy · #Amplitude #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Gaussian #Laser-Matter Interactions and Applications #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Quantum #Quantum mechanics #Quantum optics and atomic interactions #Quantum tunnelling #Range (aeronautics) #Representation (politics) #Scattering #Semiclassical physics #Statistical physics #Wave packet #quant-ph
paper · pdf · doi:10.1038/s41598-022-07599-1
arxiv created 2022/03/08 · openalex publication_date 2022/03/09 · arxiv updated 2022/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. In the picture used, the transmitted wave packet results from interference between the copies of the freely propagating state with different spatial shifts (delays), x', induced by the scattering potential. The Uncertainty Principle precludes relating the particle's final position to the delay experienced in the potential, except in the classical limit. Beyond this limit, even defining an effective range of the delay is shown to be an impracticable task, owing to the oscillatory nature of the corresponding amplitude distribution. Our examples include the classically allowed case, semiclassical tunnelling, delays induced in the presence of a virtual state, and scattering by a low barrier. The properties of the amplitude distribution of the delays, and its pole representation are studied in detail.