2017 Fiscal Year Final Research Report
Analysis of Spectral Gaps of Periodic Schroedinger Operators
| Project/Area Number |
25800085
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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 | Maebashi Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 関数解析学 / 微分方程式論 / シュレディンガー方程式 / 量子グラフ / カーボンナノチューブ / 周期ポテンシャル / バンド構造 / スペクトラルギャップ |
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| Outline of Final Research Achievements |
In this study, we dealt with the spectral theory on Schroedinger equations, which is a fundamental equation in the field of quantum mechanics. Most of the reuslts on this study are the results on spectra of periodic Schroedinger operators on a hexagonal lattice with cylindrical nanostructure, corresponding to a carbon molecule called a carbon nanotube. In this study, H. Niikuni defined the operator as a self-adjoint differential operators on graph, and examined its spectrum from the point of view of the theory of a quantum graph. On behalf of the paper on the spectra of Schroedinger operators on periodically broken carbon nanotubes, H. Niikuni published 6 related papers during the period of this study.
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| Free Research Field |
解析学
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