Comparison of the Chebyshev Method and the Generalized Crank-Nicholson Method for time Propagation in Quantum Mechanics

摘要

We compare efficiency of two methods for numerical solution of the time-dependent Schrodinger equation, namely the Chebyshev method and the recently introduced generalized Crank-Nicholson method. As a testing system the free propagation of a particle in one dimension is used. The space discretization is based on the high-order finite diferences to approximate accurately the kinetic energy operator in the Hamiltonian. We show that the choice of the more effective method depends on how many wave functions must be calculated during the given time interval to obtain relevant and reasonably accurate information about the system, i.e. on the choice of the time step.