Boscain, U.; Chambrion, T.; Gauthier, J.-P. On the \(K+P\) problem for a three-level quantum system: Optimality implies resonance. (English) Zbl 1022.53028 J. Dyn. Control Syst. 8, No. 4, 547-572 (2002). The authors develop a geometric approach in studying an optimal control problem whose general complex setting is related to the time dependent Schrödinger equation. The main result shows that the optimality implies resonance. Optimal trajectories reaching the final target and satisfying transversality conditions are computed by using methods of sub-Riemannian geometry on Lie groups. Reviewer: Dumitru Motreanu (Perpignan) Cited in 16 Documents MSC: 53C17 Sub-Riemannian geometry 49J15 Existence theories for optimal control problems involving ordinary differential equations 22E70 Applications of Lie groups to the sciences; explicit representations Keywords:sub-Riemannian geometry; Lie groups; quantum control PDFBibTeX XMLCite \textit{U. Boscain} et al., J. Dyn. Control Syst. 8, No. 4, 547--572 (2002; Zbl 1022.53028) Full Text: DOI arXiv