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The goal of this paper is to provide an analysis of the toolkit method used in the numerical approximation of the time-dependent Schrodinger 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.
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations
The three-dimensional Schrodinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order supercharges is obtai
In this work, we study the Schrodinger equation $ipartial_tpsi=-Deltapsi+eta(t)sum_{j=1}^Jdelta_{x=a_j(t)}psi$ on $L^2((0,1),C)$ where $eta:[0,T]longrightarrow R^+$ and $a_j:[0,T]longrightarrow (0,1)$, $j=1,...,J$. We show how to permute the energy a
Recently two approximate Newton methods were proposed for the optimisation of Markov Decision Processes. While these methods were shown to have desirable properties, such as a guarantee that the preconditioner is negative-semidefinite when the policy
In this paper we prove an approximate controllability result for the bilinear Schrodinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrodinger operator than those present in the lite