| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
(1) We give an explicit formula for the scattering amplitude for the Schroedinger operator with two-point delta-like magnetic fields satisfying the magnetic quantization condition, and give a numerical calculation for the amplitude. The obtained results are consistent with the asymptotic formula by Ito and Tamura. Moreover, we give an explicit formula for the spectral shift function for that model.
(2) We give a dispersive estimate for the Kronig-Penney model, which is an explicitly solvable model for the one-dimensional periodic quantum system. The estimate consists of two terms; one has the usual decay t to the power -1/2, and another has the slower decay t to the power -1/3. We also give a decay estimate for the coefficient of the latter term, with respect to the band number of the model.
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