Singularities of the Schrodinger equation
Project/Area Number |
21740090
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Single-year Grants |
Research Field |
Basic analysis
|
Research Institution | University of Tsukuba |
Principal Investigator |
ITO Kenichi 筑波大学, 数理物質系, 講師 (90512509)
|
Project Period (FY) |
2009 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 関数方程式 / 数理物理 / 関数方程式論 / リーマン多様体 / スペクトル幾何 / シュレーディンガー方程式 / 差分方程式 / 多体問題 / 超局所解析学 |
Research Abstract |
I discussed the propagation of singularities and the spectral and scattering theory for the Schrodinger operator on a noncompact manifold with ends. Iextended results on the Euclidean space to those manifolds and studied what geometric structure is essentially needed for such analysis. I found that the existence of an endand its volume growth rate can be rephrased in terms of the existence of an unbounded convex function and its strength of convexity, respectively, and formulated geometrically, without coordinates, one model manifold on which methods of the Schrodinger operator theory applies.
|
Report
(5 results)
Research Products
(45 results)