非齐次薛定谔方程的Talbot效应  

Talbot effect for the non-homogeneous Schrodinger equation

作　　者：尹子涵 康静 屈长征 YIN Zihan;KANG Jing;QU Changzheng(School of Mathematics,Northwest University,Xi'an 710127,China;School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]西北大学数学学院,陕西西安710127 [2]宁波大学数学与统计学院,浙江宁波315211

出　　处：《纯粹数学与应用数学》2025年第1期1-12,共12页Pure and Applied Mathematics

基　　金：国家自然科学基金(12371252,12431008);西北大学优博基金(2024006).

摘　　要：Talbot效应可由齐次薛定谔方程周期初边值问题的解来描述。本文主要研究非齐次薛定谔方程的Talbot效应.利用一维和二维薛定谔方程周期初边值问题Fourier级数的形式精确解,证明了非齐次薛定谔方程周期解在有理时刻可以表示为初值的有限线性组合,非齐次项的积分变换的有限线性组合以及连续函数三项和的形式.这表明在非齐次薛定谔方程中存在不同于齐次薛定谔方程新的色散复苏现象.The Talbot effect can be described by the solution to the periodic initial-boundary value problem of the homogeneous Schrodinger equation.In this paper,the Talbot effect of non-homogeneous Schrodinger equation is studied.By using the exact solutions in the form of Fourier series for the periodic initial-boundary value problems of one-dimensional and two-dimensional Schrodinger equations,it is proved that the periodic solution of the non-homogeneous Schrodinger equation at rational times can be expressed as the sum of a finite linear combination of the initial values,a finite linear combination of the integral transforms of the non-homogeneous term,and a continuous function.It implied that the existence of a new dispersive revival phenomenon in the non-homogeneous Schrodinger equation,which is different from that in the homogeneous Schrodinger equation.

关 键 词：非齐次薛定谔方程 周期初边值问题 FOURIER级数 TALBOT效应 色散复苏 

分 类 号：O175[理学—数学]