Mathematical Analysis of Quantum Physics

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340029
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Gakushuin University
• Principal Investigator: YAJIMA Kenji 学習院大学, 理学部, 教授 (80011758)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: シュレーディンガー方程式 / 初期値問題 / 散乱理論 / 波動作用素 / 量子力学 / 偏微分方程式

Outline of Final Research Achievements

Small particles like electrons and atoms are described by quantum mechanics and their dynamics is governed by Schrodinger equations which are partial differential equations for complex valued functions. The reporter studied the initial value problem for Schrodinger equations and, he has found very general sufficient conditions on inter-particle and external forces acting on the particles for the equation to generate a unique dynamics of the particles. The wave operators of the scattering theory for the Schrodinger equations, which describe the large time behavior of the particles, play important roles in various other topics of analysis. The reporter simultaneously studied the wave operators and has found various mathematically important properties such as the continuity as mapping from suitable function spaces.

Free Research Field

関数解析学、数理物理、偏微分方程式