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Burkhard Schmidt

About temporal discretization in the Matlab/Octave version of WavePacket

To understand the basic concept of temporal discretization as used in the Matlab/Octave version of WavePacket, consider the follow lines of input

time.steps.m_start = 000;            
time.steps.m_stop  = 010;            
time.steps.m_delta = 0.5; 
time.steps.s_number = 050;

Here, m_start and m_stop specify the index of the first and last time of the main time steps, the size of which are given by (constant!) m_delta. Note that the main time steps are the time intervals after which expectation values of observables are calculated and printed to console and/or logfile, and optionally the densities (from wave functions or trajectories) are plotted and/or saved. This has to be distinguished from the sub-steps or propagation time steps which are usually much smaller. They give the time stepping (time discretization) for actually propagating the wave functions or trajectories using the respective numeric schemes called in qm_propa. Their number (per main step!) is given by parameter s_number, see also here. Hence, in the example given above, a state is propagated from t=0 to t=5 in 10 main time steps, using an internal sub-step size of 0.01.

For a more in-depth explanation of how to optimally choose the time steps, along with a discussion of truncating the Hamiltonian in WavePacket, the interested reader is referred to our Wiki page on these issues.


Related

Wiki: Reference.Programs.qm_propa

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