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We study the computability of global solutions to linear Schr\"odingerequations with magnetic fields and the Hartree equation on $\mathbb R^3$. Weshow that the solution can always be globally computed with error control onthe entire space if there exist a priori decay estimates in generalized Sobolevnorms on the initial state. Using weighted Sobolev norm estimates, we show thatthe solution can be computed with uniform computational runtime with respect toinitial states and potentials. We finally study applications in optimal controltheory and provide numerical examples.

Computability of magnetic Schr\"odinger and Hartree equations on unbounded domains