1998 Fiscal Year Final Research Report Summary
Inverse scattering problems for Dirac equations
| Project/Area Number |
09640182
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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 |
解析学
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| Research Institution | Ehime University (1998)
Kyoto University (1997) |
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Principal Investigator |
ITO Hiroshi Ehime University, Fuculty of Engineering, Assistant Professor, 工学部, 助教授 (90243005)
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| Co-Investigator(Kenkyū-buntansha) |
SHIMADA Shinichi Setsunan University, Fuculty of Engineering, Assistant Professor, 工学部, 助教授 (40196481)
OKAJI Takashi Kyoto University, Graduate School of Science, Assistant Professor, 大学院理学研究科, 助教授 (20160426)
IWATSUKA Akira Kyoto Institute of Technology, Faculty of Textile of Science, Professor, 繊維学部, 教授 (40184890)
IGARI Katsujyu Ehime University, Fuculty of Engineering, Professor, 工学部, 教授 (90025487)
SADAMATSU Takashi Ehime University, Fuculty of Engineering, Professor, 工学部, 教授 (10025439)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Dirac equation / scattering operator / scattering theory / inverse scattering theory / relativistic quantum mechanics / relativistic Schrodinger equation |
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| Research Abstract |
We have considered an inverse scattering problem for Dirac equations with a time-dependent electromagnetic field. In this work it has been shown that some part of the electromagnetic field can be reconstructed from the scattering operator. Moreover, we have shown that the field can be completely reconstructed if the field is time-independent or satisfies some exponential decay condition. Our assumptions and results are independent of a choice of inertial frames, which is important for the relativistic theory. We have also shown that a similar result holds for a relativistic Schrodinger equation. The study for Schrodinger and Pauli equations is important for that of Dirac equations. Iwatsuka has studied the asymptotic distribution of eigenvalues for Pauli operators with Hideo Tamura. Okaji has shown, with De Carli, that the strong unique continuation property holds for Dirac operators with scalar potentials. Shimada has investigated Schrodinger equations with a potential supported in a line. Igari has studied the propagation of the singularities of a solution for some Cauchy problem in a complex domain. Sadamatsu has obtained a necessary condition for the well-posedness for initial value problems for some degenerate parabolic equations.
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Research Products
(20 results)
