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

Formánek, M.; Váňa, M.; Houfek, K.

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.
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
files:
aipconfproc 1281, vol 1 (2010) 667 (formanek,vana,houfek).pdf (224.57 kB)

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