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On the \(K+P\) problem for a three-level quantum system: Optimality implies resonance. (English) Zbl 1022.53028

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.

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
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