Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schrödinger equation.
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.
Tremblay
Jean Christophe
JC
Département de chimie, Université de Montréal, Case postale 6128, succursale Centre-ville, Montréal (Québec) H3C 3J7, Canada. jc.tremblay@umontreal.ca
Carrington
Tucker
T