Qualitative and quantitative analysis of solution to Schrodinger equations
Project/Area Number |
25800083
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Mathematical analysis
|
Research Institution | Osaka University (2014-2017) Gakushuin University (2013) |
Principal Investigator |
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Project Period (FY) |
2013-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | シュレディンガー方程式 / ストリッカーツ評価 / 散乱理論 / 偏微分方程式 / 時空間評価 / シュレディンガー作用素 / スペクトル理論 / 非自己共役作用素 / 漸近的錐多様体 / 半古典理論 / 超局所解析 / 捕捉軌道 / レゾルベント評価 / 平滑化作用 / 平滑化効果 |
Outline of Final Research Achievements |
A mathematical analysis of Schrodinger equation, describing the motion of particles in quantum mechanics, has been developed. We have studied effects of the behavior of external electromagnetic potentials and Hamilton flows to the behavior of the solution of Schrodinger equation, through several space-time norm inequalities. In particular, we have constructed a unified approach to deal with both the asymptotically flat metric and unbounded electromagnetic potentials. As a consequence, Strichartz estimates without loss of derivatives have been shown for such a mixed case.
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Report
(6 results)
Research Products
(23 results)