2022 Fiscal Year Final Research Report
Scattering theory and continuum limits of discrete Schrodinger operators
| Project/Area Number |
21K20337
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund |
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| Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Yukihide Tadano 東京理科大学, 理学部第一部数学科, 助教 (90908427)
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| Project Period (FY) |
2021-08-30 – 2023-03-31
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| Keywords | 離散シュレディンガー作用素 / スペクトル・散乱理論 / 連続極限 / 格子 |
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| Outline of Final Research Achievements |
Discrete Schrodinger describe behaviors of free electrons in a crystalline solid, as well as they are regarded as the discretization of the Schrodinger operators. In this research, I have studied the spectral and scattering theory of discrete Schrodinger operators and some other discrete models, e.g., quantum graphs and quantum walks, which tells us similar and different features of them when compared to continuum Schrodinger operators.
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| Free Research Field |
スペクトル・散乱理論
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の対象である離散シュレディンガー作用素および量子グラフ，量子ウォークは応用上重要な数理モデルとして知られており，本研究はこれらの数理モデルの元になった現象の理解を深めると考えられる．また，離散シュレディンガー作用素の連続極限を数学的に厳密に扱った研究は非常に少なく，本研究の結果は連続系のシュレディンガー作用素の固有値，固有ベクトルの数値計算の理論面からの正当化の一助になると考えられる．
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