2009 Fiscal Year Final Research Report
Mathematical Analysis of Quantum Physics
| Project/Area Number |
18340041
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Gakushuin University |
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Principal Investigator |
YAJIMA Kenji Gakushuin University, 理学部, 教授 (80011758)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIWARA Daisuke 学習院大学, 理学部, 教授 (10011561)
NAKAMURA Shu 東京大学, 大学院・数理科学研究科, 教授 (50183520)
MIZUTANI Akira 学習院大学, 理学部, 教授 (80011716)
WATANABE Kazuo 学習院大学, 理学部, 助教 (90260851)
SHIMOMURA Akihiro 首都大学東京, 大学院・理工学研究科, 准教授 (00365066)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 関数方程式 / 関数解析 / 実解析 |
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| Research Abstract |
We studied mathematical problems on Schroedinger equations which are fundamental equation for describing the dynamics of quantum particles and obtained following results : (1) New results are obtained on the behavior at infinity of the fundamental solutions of the initial value problems ; (2) new methods for studying the propagation of singularities of solutions are found ; (3) unsolved problems on wave operators of scattering have been solved ; (4) new spectral properties of random Schroedinger operators are found.
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