Research on Schroedinger equations by wave packet transform

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400183
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: Kato Keiichi 東京理科大学, 理学部, 教授 (50224499)
• Co-Investigator(Renkei-kenkyūsha): Ito Shingo 北里大学, 一般教育, 教授 (40548145) ; Kobayashi Masaharu 北海道大学, 大学院理学研究科, 准教授 (30516480)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 波束変換 / Wave packet transform / Schroedinger equation / Modulation space / Wave front set / Harmonic oscillator

Outline of Final Research Achievements

By using the representation of solutions to Schroedinger equations in terms of wave packet transform given by the representative of this research project and the co-workers, the representative and the co-workers has studied properties of solutions to Schroedinger equations. More precisely, we have characterize singularities to Schroedinger equations with time dependent sub-quadratic potentials and for purturbed harmonic oscillator in terms of information of
initial data.
We have studied existence and completeness of wave operators for Schroedinger equations with time dependent potentials. We have shown existence and completeness of wave operator for Schroedinger equations with time dependent shortrange potentials.

Free Research Field

偏微分方程式