2013 Fiscal Year Final Research Report
Study of algebraic structure and geometric structure of Schroedinger equations on symmetric spaces
| Project/Area Number |
23540243
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Okayama University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAMURA Hideo 岡山大学, 自然科学研究科, 名誉教授 (30022734)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Hirofumi 岡山大学, 自然科学研究科, 教授 (40192794)
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| Project Period (FY) |
2011 – 2013
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| Keywords | シュレディンガー方程式 / 対称空間 / 基本解 / 磁場 / ガウス和 |
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| Research Abstract |
We mainly studied the detailed structure of the fundamental solution to the Schroedinger equation on compact symmetric spaces from the point of view of number theory and representation theory. One of our main results is as follows. Under certain assumptions on the vector potential and on compact symmetric spaces, the singular support of the fundamental solution to the magnetic Schroedinger equation becomes a lower dimensional subset of the compact symmetric space, which is given in terms of generalized Gauss sums at a rational time. On the other hand, at an irrational time, the singular support of the fundamental solution coincides with the whole symmetric space.
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Research Products
(11 results)
