2003 Fiscal Year Final Research Report Summary
Further Development of Trotter-Kato Product Formula in Operator Norm and Related Problems on Path Integral
| Project/Area Number |
13440044
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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 |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
ICHINOSE Takashi Kanazawa University, Faculty of Science, Prof., 理学部, 教授 (20024044)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIWARA Daisuke Gakushuin University, Faculty of Science, Prof., 理学部, 教授 (10011561)
TAKANOBU Satoshi Kanazawa University, Graduate School of Natural Science and Technology, Assoc.Prof., 自然科学研究科, 助教授 (40197124)
TAMURA Hiroshi Kanazawa University, Faculty of Science, Assoc.Prof., 理学部, 助教授 (80188440)
YAJIMA Kenji Gakushuin University, Faculty of Science, Prof., 理学部, 教授 (80011758)
TAMURA Hideo Okayama University, Faculty of Science, Prof., 理学部, 教授 (30022734)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Trotter product formula / Trotter-Kato product formula / Lie-Trotter product formula / Path integral / Schrodinger operator / quantum mechanics |
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| Research Abstract |
The research is primarily motivated by B.Helffer's work 1994-5 on the Kac transfer operator as well as Rogava's work in 1993 on the selfadjoint Trotter-Kato product formula in operator norm.
(1)Ichinose and Hideo Tamura proved a very general result to the effect that the selfadjoint Trotter-Kato product formula holds in operator norm if the operator sum of two nonnegative selfadjoint operators is selfadjoint, and also, with Hiroshi Tamura and V.A.Zagrebnov, this result with optimal error boundO(1/n).
(2)Further, for the form sum case, Ichinose proved, with H.Neidhardt and V.A.Zagrebnov, the selfadjoint Trotter-Kato product formula in operator norm with optial error bound, in case where one of these operators is form-bounded with respect to the other, with some additional condition on the domains of these operators.
(3)Hideo Tamura also studied with Hiroshi Ito the 2-dimensional magnetic Schrodinger operator to watch the Aharanov-Bohm effect through the asymptotic behaviour of the scattering amplitude.
(4)Yajima studied local time-dcay of solutions of the time-periodic Schrodinger equation and the Nelson model in nonrelativistic quantum electrodynamics.
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