| 椭圆型方程哈密顿本征解的完备性 |
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| 引用本文： | 钟万勰.椭圆型方程哈密顿本征解的完备性[J].大连理工大学学报,2004,44(1):1-6. |
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| 作者姓名： | 钟万勰 |
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| 作者单位： | 大连理工大学,工业装备结构分析国家重点实验室,辽宁,大连,116024 |
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| 基金项目： | 国家重点基础研究发展规划项目(G1999032805)，国家自然科学基金资助项目(10372019)，教育部博士学科点专项科研基金资助项目(20010141024). |
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| 摘 要： | 椭圆型偏微分方程导向哈密顿对偶方程而分离变量,将导致哈密顿算子矩阵的本征值问题.以端部影响函数为核的积分方程的本征解为基底,采用有限维半解析法,再导出对偶微分方程,及其Riccati代数方程,给出半无限区段的最小总势能.采用哈密顿型的本征解展开法求解之.将有限维的结果取极限,从而证明偏微分方程本征向量函数的完备性定理.
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| 关 键 词： | 椭圆型偏微分方程 哈密顿对偶体系 本征解 共轭辛正交归一 完备性 |
| 文章编号： | 1000-8608(2004)01-0001-06 |
| 修稿时间： | 2003年9月15日 |
Completeness of eigen-solutions of elliptic PDE of Hamilton type |
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| ZHONGWan-xieian ,China.Completeness of eigen-solutions of elliptic PDE of Hamilton type[J].Journal of Dalian University of Technology,2004,44(1):1-6. |
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| Authors: | ZHONGWan-xieian China |
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| Institution: | ZHONGWan-xie~*ian 116024,China ) |
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| Abstract: | The elliptic PDE is derived to Hamilton dual equation form and then the method of separation of variables is applied, which derives to eigen-problem of Hamilton dual equation. The adjoint symplectic ortho-normality relation among eigen-solutions is proved. Using the eigen-solutions of integral equation with the symmetric kernel, which is the end influence function, as the basis, the semi-analytical method is applied, for which the algebraic Riccati equation is deduced. The solution uses eigen-solutions of n-D Hamilton dual system. The minimum potential energy variational principle is used to prove the completeness theorem of the eigen-solutions. |
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| Keywords: | elliptic PDE Hamilton dual system eigen-solutions adjoint symplectic ortho-normality completeness |
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