A Fourier‐Coefficient Based Solution of an Optimal Control Problem in Quantum Chemistry

We consider an optimal control problem for the time‐dependent Schrödinger equation modeling molecular dynamics. The dynamics can be steered by interactions with a tuned laser field. The problem of designing an optimal field can be posed as an optimal control problem. We reformulate the optimization problem by using a Fourier transform of the electric field, and narrow the frequency band. The resulting problem is less memory intense, and can be solved with a superlinearly convergent quasi‐Newton method. We show computational results for a Raman‐transition example and give numerical evidence that our method can outperform the standard monotonically convergent algorithm.