Convergence Analysis on Stochastic Collocation Methods for the Linear Schr¨odinger Equation with Random Inputs  

作　　者：Zhizhang Wu Zhongyi Huang 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China

出　　处：《Advances in Applied Mathematics and Mechanics》2020年第1期30-56,共27页应用数学与力学进展（英文）

基　　金：supported by the National Key Research and Development Plan of China No.2017YFC0601801 and NSFC Project No.11871298.

摘　　要：In this paper,we analyse the stochastic collocation method for a linear Schr¨odinger equation with random inputs,where the randomness appears in the potential and initial data and is assumed to be dependent on a random variable.We focus on the convergence rate with respect to the number of collocation points.Based on the interpolation theories,the convergence rate depends on the regularity of the solution with respect to the random variable.Hence,we investigate the dependence of the stochastic regularity of the solution on that of the random potential and initial data.We provide sufficient conditions on the random potential and initial data to ensure the smoothness of the solution and the spectral convergence.Finally,numerical results are presented to support our analysis.

关 键 词：Schrodinger equation stochastic collocation methods convergence analysis uncertainty quantification 

分 类 号：O17[理学—数学]