| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Research Abstract |
In this project we consider Schrodinger operators on noncompact graphs which consist of some infinite rays and compact part attached. Spectral and scattering problems on graphs arise as simplified models in mathematics, physics, chemistry and engineering when one considers the propagation of waves of different natures in thin, tube-like domains. We study scattering direct and inverse problems which are important in applied physics. (1)We treat an inverse scattering problem on a graph with an infinite ray and a loop joined at one point. Reconstruction procedure is presented.(2)We consider Schrodinger operators on noncompact star-shaped graphs including some finite rays. We show that our spectral representation formula provides the time dependent formulation of the scattering theory. The scattering operator is constructed in the configuration space, and then is related to the scattering matrix in the momentum space. Corresponding inverse scattering problem is investigated.
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