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薛定谔方程的整体几何光学近似

本站小编 Free考研考试/2021-12-27

郑春雄
清华大学数学科学系, 北京 100084
收稿日期:2017-09-04出版日期:2018-06-15发布日期:2018-05-15


基金资助:国家自然科学基金(11771248,91630205)资助项目.


GLOBAL GEOMETRICAL OPTICS APPROXIMATION TO THE SCHRODINGER EQUATION

Zhang Chunxiong
Tsinghua University, Department of Mathematical Sciences, Beijing 100084, China
Received:2017-09-04Online:2018-06-15Published:2018-05-15







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整体几何光学方法是一种新的求解高频线性波动方程初值问题的渐进近似理论.该理论最初是对WKB初值数据问题提出来的.在本文中,我们将采用不同的方法,对这一方法予以重新推导,使得该理论同样适用于初值为扩展WKB函数的情形.特别地,我们将建立的理论用于薛定谔方程传播子的半经典近似上来.结果表明,整体几何光学方法提供的波场近似恰好是Kay提出的半相空间公式的一个实例.作为副产品,我们指出Van Vleck近似中起到关键作用的Maslov指标可以通过一个简单的代数关系式来确定.
MR(2010)主题分类:
65M25
35F10

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[1]李昊辰, 孙建强, 骆思宇. 非线性薛定谔方程的平均向量场方法[J]. 计算数学, 2013, 35(1): 59-66.

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