定态薛定谔算子组的Dirichlet谱估计  

Dirichlet Spectrum Estimate for System of Stationary State Schr?dinger Operator

作　　者：黄振明[1] HUANG Zhen-ming(Department of Mathematics and Physics,Suzhou Vocational University,Suzhou 215104 Jiangsu,China)

机构地区：[1]苏州市职业大学数理部

出　　处：《贵阳学院学报（自然科学版）》2019年第4期4-6,11,共4页Journal of Guiyang University：Natural Sciences

摘　　要：对定态薛定谔算子组的离散谱进行定量分析,利用算子谱的定性理论、分部积分和Young不等式等主要方法,获得了在Dirichlet边界条件下用前n个离散谱的线性组合来估计第n+1个谱上界的一个解析不等式,其界与权函数、空间维数有关,而与所论区域的几何度量、算子组中方程的个数无关,其结果是参考文献结论的进一步拓展,在量子力学中有着潜在的应用价值。Quantitative analysis of discrete spectrum for system of stationary state Schr dinger operator is considered.Under Dirichlet boundary condition,an analytic inequality estimating the upper bound of the(n+1)th spectrum by a linear combination of the former n spectra is obtained using spectrum qualitative theory of operators,integration by parts and Young inequality etc.This bound is dependent of the weight function and space dimension,but irrelevant to the geometric measure of the domain or the equation numbers in the system.The results in the bibliography are improved and extended in this paper.The conclusion has potential application value in the theory of quantum mechanics.

关 键 词：薛定谔算子组 离散谱 Rayleigh-Ritz原理 特征函数组 解析不等式 

分 类 号：O175.9[理学—数学]