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On the optimal control problem for Schrödinger equation with complex potential |
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| Authors: | Hakan Yeti?kin |
| Affiliation: | a Mustafa Kemal Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, 31500 Antakya, Hatay, Turkey b Atatürk Üniversitesi, Fen Fakültesi, Matematik Bölümü, 25240 Erzurum, Turkey |
| Abstract: | The existence and uniqueness for the solution of the problem of determining the v(x,t) potential in the Schrödinger equation  from the measured final data ψ(x,T)=y(x) is investigated. For the objective functional  , it is proven that the problem has at least one solution for α?0, and has a unique solution for α>0. The necessary condition for solvability the problem is stated as the variational principle. |
| Keywords: | Optimal control problem Schrö dinger equation Frechet differential |
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