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

Author

Listed:
  • Katharina Kormann

    (Uppsala University)

  • Sverker Holmgren

    (Uppsala University)

  • Hans O. Karlsson

    (Uppsala University)

Abstract

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.

Suggested Citation

  • Katharina Kormann & Sverker Holmgren & Hans O. Karlsson, 2010. "A Fourier-Coefficient Based Solution of an Optimal Control Problem in Quantum Chemistry," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 491-506, December.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9735-9
    DOI: 10.1007/s10957-010-9735-9
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    Cited by:

    1. Nicolosi, Gabriel & Friesz, Terry & Griffin, Christopher, 2022. "Approximation of optimal control surfaces for 2 × 2 skew-symmetric evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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