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 (KENJI Yajima) 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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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥10,000,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥1,800,000)
Fiscal Year 2009: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2008: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2006: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | 関数方程式 / 関数解析 / 実解析 / 量子力学 / シュレーディンガー作用素 / シュレーディンガー方程式 / 線形偏微分方程式 / 散乱理論 / 特異性伝播 / ファインマン経路積分 / スペクトル理論 / 数理物理学 / 関数解析学 / 偏微分方程式 / 基本解 / 経路積分 / 量子物理学 / 特異性伝播問題 / 非線形偏微分方程式 / 分散型評価 / 非線形方程式 |
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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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Report
(6 results)
Research Products
(91 results)
