| Project/Area Number |
24540176
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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 | Ehime University |
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Principal Investigator |
ITO Hiroshi 愛媛大学, 理工学研究科, 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)
NOMURA Yuji 愛媛大学, 理工学研究科, 准教授 (40282818)
IWATSUKA Akira 京都工芸繊維大学, 工芸科学研究科, 教授 (40184890)
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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 |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | ディラック作用素 / パウリ作用素 / スペクトル / レゾナンス / 非相対論的極限 / シュレーディンガー作用素 / 関数解析 / 数理物理 / 関数方程式 / 関数方程式論 |
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| Outline of Final Research Achievements |
We study the spectral properties of the Dirac operator, appeared in the relativistic quantum mechanics, with a bounded magnetic potential and an unbounded electric potential. These potentials are assumed to be analytic in some sense. We first determine the structure of the spectrum of the Dirac operator. Then, we show that if the speed of light is sufficiently large the Dirac operator has resonances (complex eigenvalues) near eingenvalues and resonances of two Pauli operators appeared in the nonrelativistic quantum mechanics.
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