We compare efficiency of two methods for numerical solution of the time-dependent Schrödinger equation, namely

the Chebyshev method and the recently introduced generalized Crank-Nicolson 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.

the Chebyshev method and the recently introduced generalized Crank-Nicolson 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.

typ: | inproceedings |
---|---|

volume: | 1 |

pages: | 667-670 |

year: | 2010 |

pacs: | 02.60.Lj, 02.70.-c, 34.10.+x, 34.80.-i |

odkaz: | http://proceedings.aip.org/resource/2/apcpcs/1281/1/667_1 |