天津师范大学学报（自然科学版）2026，Vol.46Issue(1)：1-5,5.DOI:10.19638/j.issn1671-1114.20260101
基于最优扰动正则化方法的一维薛定谔方程参数辨识
Parameter identification for one-dimensional Schrödinger equation based on optimal perturbation regularization method
摘要
Abstract
The parameter identification of one-dimensional Schrödinger equation through boundary control and boundary ob-servation is studied.Firstly,the identifiability of the diffusion coefficient is proven by virtue of inverse spectral theory and In-gham-Beurling theorem.It should be noted that the required observation time for identification can be arbitrarily short.Subse-quently,based on the optimal perturbation regularization method,an algorithm is presented to reconstruct the unknown pa-rameter of the Schrödinger equation.Finally,the effectiveness of the identification algorithm is validated through some nu-merical simulations.关键词
薛定谔方程/参数辨识/逆谱理论/最优扰动正则化Key words
Schrödinger equation/parameter identification/inverse spectral theory/optimal perturbation regularization method分类
数理科学引用本文复制引用
包春莹,赵志学..基于最优扰动正则化方法的一维薛定谔方程参数辨识[J].天津师范大学学报（自然科学版）,2026,46(1):1-5,5.基金项目
国家自然科学基金资助项目(12326327,11901433). （12326327,11901433）
