2006/09/25 by O. Costin, Ovidiu Costin, Costin, O. +6 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Atomic and Molecular Physics #FOS: Physical sciences #Ion-surface interactions and analysis #Mathematical Physics (math-ph) #Quantum optics and atomic interactions #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0609069
Corrected proof, extensive changes. 39 pages, 1 figure
openalex publication_date 2006/09/25 · arxiv created 2007/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the evolution of a one dimensional model atom with δ-function binding potential, subjected to a dipole radiation field E(t) x with E(t) a 2π/ω-periodic real-valued function. Starting with ψ(x,t=0) an initially localized state and E(t) a trigonometric polynomial, complete ionization occurs; the probability of finding the electron in any fixed region goes to zero. For ψ(x,0) compactly supported and general periodic fields, we construct a resonance expansion. Each resonance is given explicitly as a Gamow vector, and is 2π/ω periodic in time and behaves like the exponentially growing Green's function near x=± ∞. The remainder is given by an asymptotic power series in t-1/2 with coefficients varying with x.