2003/01/22 by N. L. Chuprikov, Chuprikov, N. L.
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Physical sciences #Microwave and Dielectric Measurement Techniques #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0301113
13 pages, revtex, no figures
openalex publication_date 2003/01/22 · arxiv created 2003/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A complete one-dimensional scattering of a spinless particle on a time-independent potential barrier is considered. To describe separately transmitted and reflected particles in the corresponding subsets of identical experiments, we introduce the notions of scattering channels for transmission and reflection. We find for both channels the (unitary) scattering matrices and reconstruct, by known out asymptotes (i.e., by the transmitted and reflected wave packets), the corresponding in asymptotes. Unlike the out asymptotes for transmission and reflection, their in asymptotes represent nonorthogonal functions. As is shown, the position distributions of to-be-transmitted and to-be-reflected particles, except their average positions, are unpredictable. At the same time, the momentum distributions of these particles are physically meaningful and can be observed to the full. We show that both the subensembles of particles must start (on the average) from the same spatial point, and the momentum distributions of to-be-scattered and scattered particles must be the same for each scattering channel. Taking into account these properties, we define the (individual) delay times for transmission and reflection for wave packets of an arbitrary width. Besides, to estimate the duration of the scattering event, we derive the expression for a (total) scattering time.