Research Information System
Applied Mathematics and Computation, vol.216, no.7, pp.1896-1902, 2010 (SCI-Expanded, Scopus)
The existence and uniqueness for the solution of the problem of determining the v (x, t) potential in the Schrödinger equation i frac(∂ ψ, ∂ t) + frac(∂, ∂ x) fenced(a0 (x) frac(∂ ψ, ∂ x)) - a (x) ψ + iv (x, t) ψ = f (x, t) from the measured final data ψ (x, T) = y (x) is investigated. For the objective functional Jα (v) = {norm of matrix} ψ (x, T ; v) - y (x) {norm of matrix}L2 (0, ℓ)2 + α {norm of matrix} v - w {norm of matrix}W20, 1 (Ω)2, 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. © 2010 Elsevier Inc. All rights reserved.