SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Splitting methods for Schrödinger equations in imaginary time

P. Bader, S. Blanes and F. Casas

An efficient method to compute the eigenstates of the Schrödinger equation is the propagation in imaginary time. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order greater than two necessarily have negative steps and can not be used for this class of diffusive problems. However, there exist methods which use fractional complex time steps with positive real parts which can be used with only a moderate increase in the computational cost. We analyze the performance of this class of schemes and propose new methods which outperform the existing ones in most cases. If the gradient of the potential is available, methods up to fourth-order with real and positive coefficients exist. We also explore this problem class and present highly optimized sixth order schemes for near integrable systems using positive real part complex coefficients with and without modified potentials.

Organized by         Universidad de Valladolid     IMUVA