|Budget Amount *help
¥13,260,000 (Direct Cost: ¥10,200,000、Indirect Cost: ¥3,060,000)
Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2012: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
|Outline of Final Research Achievements
We have succeeded in concretely describing the singularity structure of the Borel transformed WKB solutions of several basic one-dimensional Schroedinger equations near their fixed singular points. The main tool for the description is the so-called alien calculus, and the idea is based on the role of a bicharacteristic strip as a carrier of singularities of solutions of linear partial differential equations. Thus our result is an outcome of the complementality of microlocal analysis and the exact WKB analysis. We have also studied higher order ordinary differential equations with a large parameter through its Borel transform ; a virtual turning point is an indispensable ingredient in the exact WKB analysis of higher order equations.
Kawai and Takei, with the collaborator N. Honda(Hokkaido University) published a monograph titled “Virtual Turning Points”(Springer ; 2015), so that this novel notion may be widely appreciated by mathematical physicists and engineers.