| Project/Area Number |
15K04959
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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 | Ehime University |
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Principal Investigator |
Ito Hiroshi 愛媛大学, 理工学研究科(工学系), 教授 (90243005)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Osanobu 立命館大学, 理工学部, 教授 (70066744)
TAMURA Hideo 岡山大学, 理学部, 教授 (30022734)
IWATSUKA Akira 京都工芸繊維大学, 工芸科学研究科, 教授 (40184890)
NOMURA Yuji 兵庫県立大学, 物質理学研究科, 教授 (40282818)
MINE Takuya 京都工芸繊維大学, 工芸科学研究科, 教授 (90378597)
ANDO Kazunori 愛媛大学, 理工学研究科, 准教授 (70774884)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | ディラック作用素 / パウリ作用素 / レゾナンス / 非相対論的極限 / 関数解析 / 数理物理 / 関数方程式 |
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| Outline of Final Research Achievements |
The purpose of this work is to study the spectral properties and resonances (complex eigenvalues) of Dirac operators and relativistic Pauli operators, which are important Hamiltonians in the relativistic quantum mechanics, with a bounded magnetic potential and an unbounded electric potential. We also assume that these potentials are dilation analytic. We first study their spectral properties by using the complex scaled Hamiltonians, and then obtain some resonance-free-region.Moreover, we show that each resonance converges to a resonance (or eigenvalue) of the corresponding Pauli operator as the velocity of light goes to infinity.
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