Many numerical simulations in (bilinear) quantum control use the monotonically convergent Krotov algorithms (introduced byTannor et al. [Time Dependent Quantum Molecular Dynamics (1992) 347–360]), Zhu and Rabitz [J. Chem. Phys. (1998) 385–391] or theirunified form described in Maday and Turinici [J. Chem. Phys. (2003) 8191–8196]. InMaday et al. [Num. Math. (2006) 323–338], a time discretization which preserves theproperty of monotonicity has been presented. This paper introduces aproof of the convergence of these schemes and some results regarding theirrate of convergence.
