Yetiskin, HakanSubasi, Murat2024-09-182024-09-1820100096-3003https://doi.org/10.1016/j.amc.2010.03.039https://hdl.handle.net/20.500.12483/11480The existence and uniqueness for the solution of the problem of determining the v(x, t) potential in the Schrodinger equation i partial derivative psi/partial derivative t + partial derivative/partial derivative x (a(0)(x)partial derivative psi/partial derivative x) - a(x)psi + iv(x, t)psi = f(x, t) from the measured final data psi(x,T) = y(x) is investigated. For the objective functional J(alpha)(nu) = parallel to psi(x, T; v) - y(x)parallel to(2)(L2)(0,l) + alpha parallel to nu - w parallel to(2)(W2)0,1 (Omega), it is proven that the problem has at least one solution for a alpha >= 0, and has a unique solution for alpha > 0. The necessary condition for solvability the problem is stated as the variational principle. (C) 2010 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessOptimal control problemSchrodinger equationFrechet differentialArticle21671896190210.1016/j.amc.2010.03.0392-s2.0-77953230857Q1WOS:000277703300002Q1