2012 Fiscal Year Final Research Report
SPECTRALANALYSISOFQUANTUMHAMILTONIANSATTHRESHODENERGIES
| Project/Area Number |
21540193
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | University of Hyogo |
|---|
Principal Investigator |
UMEDA Tomio 兵庫県立大学, 大学院・物質理学研究科, 教授 (20160319)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
IWASAKI Chisato 兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
HOSHIRO Toshihiko 兵庫県立大学, 大学院・物質理学研究科, 教授 (40211544)
FUJIIE Setsuro 兵庫県立大学, 大学院・物質理学研究科, 准教授 (00238536)
|
|---|
| Project Period (FY) |
2009 – 2012
|
| Keywords | 関数方程式 / スペクトル理論 / 固有関数 |
|---|
| Research Abstract |
We investigated mathematical properties of energies of Dirac operators, which play fundamental roles in quantum mechanics, describing states of tiny particles like atoms. We found a few of new mathematical phenomena on threshold energies which are considered to be clues in theoretical explanations of the electron-positron pair creation. We also found an infinite series of functions, which play significant roles in the theoretical treatments of stability of matter. In addition, we discovered a mathematical phenomenon in connection with some important inequalities and with some important functions at threshold energies.
|
