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Quantum mechanics in 1D.

Project description

The quantum_dynamics package contains tools for simulation of 1D time-dependent Schrödinger equation. The package allows for simulation of 1D model potentials and time-dependent external interactions, e.g., an laser electric field in the dipole approximation.

This package has been created as a reference solution to an exercise in the computational physics course at Tampere University of Technology in Spring 2018.

The key numerical methods behind the package are:

  1. finite-difference approximation of the laplacian operator with Dirichlet boundary conditions at the endpoints of the simulation grid
  2. exponential mid-point rule for the time-evolution operator
  3. krylov-subspace based implementation of the matrix exponential
Upon successful installation, two executables are copied to your PATH:
  • qdyn_laser
  • plot_time_evolution


This simulates the electron in 1D soft coulomb potential (“1D hydrogen”) under laser electric field with sin^2 envelope and cosine carrier wave. Please consult the help of the script for all options: qdyn_laser --help.

After a successful simulation, an outputfile of HDF5-format is created. It contains the following datasets and groups

The gridpoints of the coordinate space used in the calculation.
The times corresponding to the saved wavefunction values in the file.
A 2D array of values of the wavefunction. The first index corresponds to coordinate_grid and the second index to savetimes.
Wavefunction values at the end of the simulation.
The laser electric field for all timesteps. First column is times, second the laser electric field values.

The time-independent part of the Hamiltonian matrix. It’s saved as a sparse matrix and can be loaded with quantum_dynamics.utils.load_sparse_matrix like:

from quantum_dynamics.utils import load_sparse matrix
import h5py

with h5py.File("myfile.h5", "r") as f:
    H0 = load_sparse_matrix(f['tise_hamiltonian'])


This can be used to visualize the time-evolved density calcualted with qdyn_laser. For usage instructions, please see plot_time_evolution --help.


Janne Solanpää

Project details

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