2008/09/24 by Chyi-Lung Lin, Lin, Chyi-Lung, Meng-Jie Huang +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Nonlinear Photonic Systems #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.48550/arxiv.0809.4105
arxiv created 2008/09/24 · openalex publication_date 2008/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss nonspreading wave packets in one dimensional Schrödinger equation. We derive general rules for constructing nonspreading wave packets from a general potential \textmdV(x,t). The essential ingredients of a nonspreading wave packet, the shape function f(x), the motion d(t), the phase function ϕ(x,t) are derived. Since the form of the shape of a nonspreading wave packet does not change in time, the shape equation should be time independent. We show that the shape function f(x) is the eigenfunction of the time independent Schrödinger equation with an effective potential V_\textmdeff and an energy E_\textmdeff. We derive nonspreading wave packets found by Schrödinger, Senitzky, and Berry and Balazs as examples. We show that most stationary potentials can only support stationary nonspreading wave packets. We show how to construct moving nonspreading wave packets from time dependent potentials, which drive nonspreading wave packets into an arbitrary motion.