无界Schr?dinger算子的谱分布与相应能量泛函的分解研究综述  

Review on Spectrum of Unbounded Schr?dinger Operator and Resolutions of Corresponding Energy Functional

作　　者：穆超[1] 李成岳[1] 张卫杰 MU Chao;LI Chengyue;ZHANG Weijie(College of Science,Minzu University of China,Bejing 100081,China;The ffiliated High School to the Minzu University of China,Bejing 100081,China)

机构地区：[1]中央民族大学理学院,北京100081 [2]中央民族大学附属中学,北京100081

出　　处：《中央民族大学学报（自然科学版）》2020年第1期19-23,共5页Journal of Minzu University of China(Natural Sciences Edition)

基　　金：中央民族大学研究生自主科研项目(SSZZKY-2019100)

摘　　要：考虑无界Schrodinger算子LVu=-Δu+V(x)u与LV的平移算子L=LV-μ,这里u∈L^2(R^N),μ是实数。分三种情形:(i)V(x)→+∞,μ=λk是LV的特征值;(ii)V(x)→0,μ=λk<0是LV的特征值;(iii)V(x)是周期函数,μ是LV的正则值,分别综述算子LV与L的谱分布与相应能量泛函分解的研究结果。In this paper, we discussed with the spectrum of unbounded Schrodinger operator LV, which defined as LVu=-Δu+V(x)u, and shift operator L=LVμ, u∈L^2(R^N), μ is a parameter. We summarized some resolutions of the energy functional corresponding to the problem above, when V(x), μ satisfied three different situation,(i) V(x)→+∞, μ=λk is an eigenvalue of LV,(ii) V(x)→0, μ=λk<0 is a discrete spectrum of LV,(iii) V(x) is periodical, μ is not eigenvalue of LV.

关 键 词：SCHRODINGER算子 强不定问题 谱分布 临界点 

分 类 号：O175[理学—数学]