| Project/Area Number |
10640204
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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 |
Global analysis
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| Research Institution | KYOTO INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
IWATSUKA Akira Faculty of Textile Science, KYOTO INSTITUTE OF TECHNOLOGY Professor, 繊維学部, 教授 (40184890)
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| Co-Investigator(Kenkyū-buntansha) |
DOI Shin-ichi Institute of Mathematics, University of Tsukuba, Associate Professor, 数学系, 助教授 (00243006)
YAGASAKI Tatsuhiko Faculty of Engineering and Design, KYOTO INSTITUTE OF TECHNOLOGY Associate Professor, 工芸学部, 助教授 (40191077)
UCHIYAMA Jun Faculty of Textile Science, KYOTO INSTITUTE OF TECHNOLOGY Professor, 繊維学部, 教授 (70025401)
SHIMADA Shin-ichi Department of Mathematics and Physics, Setsunan University, Associate Professor, 工学部, 助教授 (40196481)
ITO Hiroshi Faculty of Engineering, Ehime University, Associate Professor, 工学部, 助教授 (90243005)
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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 |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1998: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Schrodinger Operator / Periodic Electromagnetic Field / Spectral Structure / Magnetic Field / Selfadjoint Extention / Aharonov-Bohm Effect / Density of States / Wavefunction / シュレディンガー作用素 / 周期的ポテンシャル |
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| Research Abstract |
To begin with, we studied the Schrodinger operators with point interactions with Shin-ichi Shimada. Namely we studied the Schrodinger operator with a magnetic point interaction at the origin known as Aharonov-Bohm effect Hamiltonian. Since this operator defined on the space of compactly supported smooth functions is not essentially selfadjoint, w determined all the self adjoint extension of this operator and their boundary conditions at the origin. We also showed that one can calculate the asymptotic completeness, the phase shift formula, the eigenfunction expansions etc. for these operators which preserves the angular momentum. We obtained expressions of the wave operators, scattering matrices and the scattering amplitudes, and showed the eigenfunction expansion formula as well. This enabled to characterize the operator treated by Aharonov and Bohm in terms of the behavior at the origin of the wavefunctions.
We also studied on the uniqueness of the integrated density of states with Shin-ichi Doi. We showed that the integrated density of states is uniquely defined independently of the way to extend the regions to the whole space or the choisce of the boundary conditions under relatively general assumptions in the presence of the magnetic fields. Also we obtained a sufficient conditions for the coincidence of the integrated density of states defined in terms of the whole space operator and that defined by using the finite region operators. This enabled to compute the spectrum of the whole space operators by calculating those of the finite region operators.
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