Reference.Programs.Main

Main functions in the Matlab/Octave version of WavePacket

All the main Matlab/Octave functions listed here are centered around the wavepacket picture of time dependent quantum mechanics, partly also classical and mixed quantum-classical mechanics: In particular, they solve the time independent and time-dependent Schrödinger equation (TISE and TDSE) as well as the (time-dependent) classical, quantum-classical or quantum Liouville-von Neumann equation (LvNE).

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• All numerical input and output of WavePacket functions is in atomic units throughout. Note that in qm_setup there is a plethora of conversion factors which you may want to use for preprocessing your input and/or post-processing your output data.

• For a quick start of your projects using WavePacket, see the demo examples available in the WavePacket central Wiki.

DVR (position) / FBR (momentum) space representation

In position/momentum representation, TDSEs are treated as partial differential equations (PDEs).

• qm_bound: Perform bound state calculations (solving the TISE)

• qm_propa: Perform wavepacket propagations (solving the TDSE or solving the CLE or solving the QCLE )

• qm_movie: Visualize results from previous (qm_bound or qm_propa) WavePacket calculations

State/energy space representation

In state/energy representation, TDSEs are treated as ordinary differential equations (ODEs).

• qm_matrix: Generate matrix (state space) representations of relevant operators

• qm_abncd: Generate necessary input for bilinear control problem

• qm_propa: Simulate bilinear control of driven quantum system (solving the TDSE or solving the LvNE in state space)

• qm_optimal: Simulate optimal control of driven quantum systems (solving the TDSE or solving the LvNE in state space)

Dimension reduction

For an introduction, see also our general Wiki page on dimension reduction

• qm_balance: Perform balancing transformation

• qm_truncate: Perform truncation of balanced representation

• qm_H2model: Perform H2 optimal model reduction (Breiten/Benner, MPI Halle)

General utilities

Run these before or after WavePacket simulations

• qm_init: Initialize your WavePacket simulations

• qm_setup: Before WavePacket simulations

• qm_cleanup: After WavePacket simulations

Auxiliary codes

These Matlab/Octave codes are (at least partly) less mature, less well documented, and less extensively tested, and partly still under development. Use with care!

• qm_rerun: Restarts an interrupted TDSE calculation at a given time step

• qm_regenerate: Regenerates some global data needed to restart a saved TDSE calculation

• qm_fcspec: Franck Condon (absorption) spectra from saved TISE calculation

• qm_correlation: Cross-correlation between two TDSE simulations

• qm_measure: Retrieve densities from bilinear control problem and get measures of correlation, entropy, entanglement

• qm_BTversusH2: Direct comparison of balanced truncation versus interpolation based H2 model reduction

• qm_H2error: Calculate H2 error from balanced truncation and/or interpolation based H2 model reduction

Flowchart

While quantum dynamics of closed systems (position representation of TDSE in PDE form) can be simulated directly using qm_propa, WavePacket offers also an alternative approach based on state representations of wavefunctions/densities, see our flowchart below. This approach can be used for quantum dynamics both of closed systems (state representation of TDSE in ODE form) or open systems (state representation of LvNE in ODE form) on an (almost) equal footing. In the latter case, dimension reduction is often mandatory to beat the curse of dimensionality.

For a detailed description of the data files mentioned in the chart, see also to our list of WavePacket data files