Semi-classical analysis of Schroedinger equations
| Project/Area Number |
24540196
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
IWASAKI Chisato 兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
UMEDA Tomio 兵庫県立大学, 大学院・物質理学研究科, 教授 (20160319)
YAMADA Osanobu 立命館大学, 理工学部, 教授 (70066744)
WATANABE Takuya 立命館大学, 理工学部, 准教授 (80458009)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 準古典解析 / シュレディンガー作用素 / 超局所解析 / WKB解析 / レゾナンス / スペクトルシフト関数 / 準古典極限 / シュレディンガー方程式 / ホモクリニック軌道 / 国際研究者交流 フランス / 国際研究者交流 イタリア |
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| Outline of Final Research Achievements |
First, I wrote down the quantization condition of resonances and clarified the asymptotic distribution of these resonances for the Schroedinger operator near an energy at which the corresponding classical mechanics has a non-degenerate hyperbolic fixed point and associated homoclinic or heteroclinic orbits as trapped set.
Second, I proved that the spectral shift function for the Stark hamiltonians has a complete asymptotic expansion at non-trapping energies.
Finally, I wrote down the quantization condition of resonances and clarified the asymptotic distribution of these resonances near a crossing level of two potentials of a system of Schroedinger operators.
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Report
(4 results)
Research Products
(16 results)
