| Project/Area Number |
09440068
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Department of Mathematics, Faculty of Sciences, Gakushuin University |
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Principal Investigator |
FUJIWARA Daisuke Gakushuin Univ., Dept.of Math. Prof., 理学部, 教授 (10011561)
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| Co-Investigator(Kenkyū-buntansha) |
ICHINOSE Takashi Kanazawa Univ., Dept.of Math. Prof., 自然科学研究科, 教授 (20024044)
KAWASAKI Tetsuro Gakushuin Univ., Dept.of Math. Assoc.Prof., 理学部, 助教授 (90107061)
KATASE Kiyoshi Gakushuin Univ., Dept.of Math. Prof., 理学部, 教授 (70080489)
MIZUTANI Akira Gakushuin Univ., Dept.of Math. Prof., 理学部, 教授 (80011716)
KURODA Shigetoshi Gakushuin Univ., Dept.of Math. Prof., 理学部, 教授 (20011463)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Feynman path integrals / Oscillatory integrals / Schrodinger equation / Perturbation / Selfajoint operator / Quantum mechanics / Feynman-Kac formula / Lie-Trotter product formula |
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| Research Abstract |
1. Fujiwara tried to give mathematically rigorous treatment of Feynman path integrals. He together with Tsuchida constructed the fundamental solution of Schrodinger equation with magnetic potentials, using oscillatory integrals over R^n with large dimension n. Fujiwara, together with K.Taniguchi and N.Kumano-go, gave a new and direct proof of Kumano-go-Taniguchi estimate for oscillatory integral over a large dimensional space.
2. S.T.Kuroda constructed self adjoint Hamiltonians with a very singular potential called point interaction type through deep analysis of resolvents. He generalized his method and succeeded in constructing any self adjoint operators through resolvents.
3. Mizutani together with T.Suzuki of Osaka Univ. proved a finite element numerical approximation converges La the true solution of degenerating nonlinear parabolic equations. Their scheme preserves order and contraction property in L^1 space.
4. Watanabe studied asymptotic behavior of scattering phase for modified scattering matrfx of Schr6dinger operators with magnetic field without spherical symmetry. Watanabe also studied spectral concentration and resonaces for Schr6dinger operators having smooth potential or potential with singularity.
5. Ichinose succeeded in proving norm estimate for the difference between Kac's transfer operator and Schr6dinger semi-group. As an application he proved the uniform operator norm convergence of Lie-Trotter product formula to the semi-group.
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