2022 Fiscal Year Final Research Report
Geometric methods for the Schrodinger equation
| Project/Area Number |
17K05325
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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 |
Mathematical analysis
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| Research Institution | The University of Tokyo (2018-2022)
Kobe University (2017) |
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Principal Investigator |
ITO Kenichi 東京大学, 大学院数理科学研究科, 准教授 (90512509)
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Keywords | シュレーディンガー作用素 / スペクトル理論 / 散乱理論 / 差分作用素 / 数理物理学 / 関数解析学 / 量子力学 |
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| Outline of Final Research Achievements |
In this research project I applied a commutator method that I had invented to the Schrodinger operators with N-body, Stark or long-range potentials, and obtained a series of results including the stationary scattering theory. In addition, I completely classified threshold resonances of the Schrodinger operator on a graph with rays. Moreover, I obtained asymptotic expansions of the resolvent around thresholds for the Laplacian on the 2-dimensional square lattice.
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| Free Research Field |
偏微分方程式論
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| Academic Significance and Societal Importance of the Research Achievements |
Schrodinger作用素のスペクトル・散乱理論に有効な新しい交換子スキームの導入に成功した．このスキームは高度な関数解析学的手法や擬微分作用素の理論を必要とせず，古典的な交換子計算のみで完結する，簡素なものである．そのため，広範な関連研究領域においてさらなる応用や発展が見込まれる．また，2次元格子状の格子Green関数に対しても新奇性の高い知見が得られた．これは今後の関連研究への足掛かりとして有用なものと期待される．
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