2017 Fiscal Year Final Research Report
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 |
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| Research Field |
Mathematical analysis
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| Research Institution | Osaka University (2014-2017)
Gakushuin University (2013) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| 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 |
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| 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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| Free Research Field |
偏微分方程式
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