Switching Controls for Conservative Bilinear Quantum Systems with Discrete Spectrum

Abstract. We analyze attainable sets of single-input bilinear conservative systems with piecewise constant controls. Under the assumption that the ambient space admits a Hilbert basis made of eigenvectors of the drift operator, we show that the closure of the attainable set does not depend on the set of admissible controls, provided the controls can take at least two or three values.