一类无穷维Hamilton算子本征函数系的完备性  

Completeness of Eigenfunction System for a Class of the Infinite Dimensional Hamiltonian Operators

作　　者：刘超群[1] 赵胤宇 张家悦 侯国林[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《数学的实践与认识》2014年第23期267-272,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11361034);内蒙古自然科学基金(2012MS0105);内蒙古大学本科生创新基金项目(20130109)

摘　　要：研究了Sturm-Liouvile偏微分方程导出的无穷维Hamilton算子的本征值问题.证明了导出的无穷维Hamilton算子族本征函数系的完备性,为对此类方程应用基于Hamilton体系的分离变量法提供了理论基础.最后举例说明了结果的有效性.The eigenvalue problem of the infinite dimensional Hamiltonian operators, which arise from the equation of Strum-Liouville type, is considered. The completeness of eigen- function system of the operators is proved, which offers the theoretical basic for the method of separation of variables for Hamiltonian system. Finally, the feasibility of the conclusions obtained is illustrated.

关 键 词：HAMILTON算子 本征函数系 完备性 Strum-Liouville 

分 类 号：O177[理学—数学]