四元数量子力学中一类特征值反问题及其应用(英文)  

One Kind of Inverse Eigenvalue Problems and its Applications in Quaternionic Quantum Mechanics

作　　者：贾志刚[1] 赵建立[1] 李莹[2] 姜同松[3] 

机构地区：[1]华东师范大学数学系,上海200062 [2]聊城大学数学科学学院,山东252059 [3]临沂师范学院数学系,山东276005

出　　处：《工程数学学报》2007年第2期343-347,共5页Chinese Journal of Engineering Mathematics

基　　金：National Science Foundation of China (10671086);Natural Science Foundation of Shandong Provence(Y2005A12).

摘　　要：本文研究了四元数量子力学中一类要求其解是正规或可对角化四元数矩阵的特征值反问题。并给出了其有解的充要条件和通解的表达式。讨论了四元数量子力学中带有谱约束的最小二乘解反问题,得到了此问题有解的充分条件。最后给出了数值算法和数值例子。One kind of inverse eigenvalue problems, whose solutions are required to be normal or diagonalizable matrices, is investigated in quaternionic quantum mechanics. A sufficient and necessary condition for the existence of solution of is determined, followed by the representation of the general solution. The inverse least square problem with spectral constraints is also studied and a sufficient condition is given for its solvability. At last a numerical algorithm and a numerical example are given.

关 键 词：正规四元数矩阵 特征值反问题 范数 谱约束 

分 类 号：O151.21[理学—数学]