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We use a posteriori error estimation theory to derive a relation between local and global error in the propagation for the time-dependent Schrödinger equation. Based on this result, we design a class of h, p-adaptive Magnus–Lanczos propagators capable of controlling the global error of the time-stepping scheme by only solving the equation once. We provide… (More)

We consider an optimal control problem for the time-dependent Schrödinger equation modeling molecular dynamics. Given a molecule in its ground state, the interaction with a tuned laser pulse can result in an excitation to a state of interest. By these means, one can optimize the yield of chemical reactions. The problem of designing an optimal laser pulse… (More)

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