Tremblay JC, Carrington T. Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schrödinger equation.
J Chem Phys 2004;
121:11535-41. [PMID:
15634118 DOI:
10.1063/1.1814103]
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Abstract
If the Hamiltonian is time dependent it is common to solve the time-dependent Schrödinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size Runge-Kutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size Runge-Kutta method is about an order of magnitude more efficient than the time sliced method.
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