| Project/Area Number |
10640194
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
YAMADA Osanobu Ritsumeikan Univ. Fac. Science and Engineering, Professor, 理工学部, 教授 (70066744)
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| Co-Investigator(Kenkyū-buntansha) |
SHINYA Hitoshi Ritsumeikan Univ. Fac. Science and Engineering, Professor, 理工学部, 教授 (70036416)
SATO Yousuke Ritsumeikan Univ. Fac. Science and Engineering, Professor, 理工学部, 教授 (50257820)
ISHII Hidenori Ritsumeikan Univ. Fac. Science and Engineering, Professor, 理工学部, 教授 (60159671)
YAMADA Toshio Ritsumeikan Univ. Fac. Science and Engineering, Professor, 理工学部, 教授 (10037749)
NARUKI Isao Ritsumeikan Univ. Fac. Science and Engineering, Professor, 理工学部, 教授 (90027376)
荒井 正治 立命館大学, 理工学部, 教授 (20066715)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Dirac operator / relativistic quantum mechanics / unique continuation property / self-adjoint operator / essentially self-adjoint / spectrum / 相対性量子力学 / Dirac作用素 / 固有値 / 連続スペクトル |
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| Research Abstract |
We are interested in spectral theory of Dirac operators,
H := ΣィイD63(/)j=1ィエD6αィイD2jィエD2 DィイD2jィエD2 + mβ+ V(x)IィイD24ィエD2( x∈RィイD13ィエD1, DィイD2jィエD2 = -IィイD7∂(/)∂xィイD2jィエD2ィエD7)
which appear in relativistic quantum mechanics. Our recent interest is in the case where the mass tern m is a scalar function. In schmidt-Yamada (Publ RIMS, Kyoto Univ., 1998) we have studies the absolutely continuous part of the spectrum of the Dirac operator in the case m(r) → ∞, and V(r) → ∞ as r → ∞ under weak conditions. In Kalf-Yamada (Proc. Japan Acad. Ser. A., 2000) we have investigated the essential self-adjointness of the Dirac operator with a singular potential and a singular mass term m(x) at the origin.
We can admit the singularity stronger than that of Coulomb potentials.
In Kalf-Yamada (Publ. RIMS, Kyoto Univ., 1999) we have given another proof for a theorem by De Carli and Okaji on the strong unique continuation property of Dirac equations.
In order to proceed these works we invited Prof. Hubert Kalf from Munichi in Germany in October, 1999.O.Yamada attended international conferences at University of Alabama at Birmingam, USA in March, 1999 and at Connam National University, Kwangju, Korea in July, 1999, and gave a lecture there.
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