Analysis of the Toolkit method for the time-dependent Schrödinger equation

Lucie Baudouin (1) , Julien Salomon (2) , Gabriel Turinici (2)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The goal of this paper is to provide an analysis of the ''toolkit'' method used in the numerical approximation of the time-dependent Schrödinger equation. The ''toolkit'' method is based on precomputation of elementary propagators and was seen to be very efficient in the optimal control framework. Our analysis shows that this method provides better results than the second order Strang operator splitting. In addition, we present two improvements of the method in the limit of low and large intensity control fields.

Keywords: Toolkit method; quantum control; time-dependent Schrödinger equation

Domains: Optimization and Control [math.OC]

Lucie Baudouin, Julien Salomon, Gabriel Turinici. Analysis of the Toolkit method for the time-dependent Schrödinger equation. Journal of Scientific Computing, 2011, 49 (2), p. 111-136. ⟨10.1007/s10915-010-9450-6⟩. ⟨hal-00403798v3⟩