2004/06/25 by A. Yahalom, R. Englman
Physics and Astronomy · #quant-ph
published as J. Phys. Chem. A, 107(37), 7170 - 7174 (2003) · 15 pages, 3 figures
arxiv created 2004/06/25 · arxiv updated 2009/12/01
We formulate analytically the reflection of a one dimensional, expanding free wave-packet (wp) from an infinite barrier. Three types of wp's are considered, representing an electron, a molecule and a classical object. We derive a threshold criterion for the values of the dynamic parameters so that reciprocal (Kramers-Kronig) relations hold \it in the time domain between the log-modulus of the wp and the (analytic part of its) phase acquired during the reflection. For an electron, in a typical case, the relations are shown to be satisfied. For a molecule the modulus-phase relations take a more complicated form, including the so called Blaschke term. For a classical particle characterized by a large mean momentum (ℏ K >> \fracℏ trajectory length (size of wave-packet)2 >>> (ℏ)/(size of wave-packet)) the rate of acquisition of the relative phase between different wp components is enormous (for a bullet it is typically 1014 GHertz) with also a very large value for the phase maximum.