Time-dependent Hartree-Fock theory#

This is a project on the time-dependent Hartree-Fock method applied to a system of two one-dimensional quantum dots for the course FYS4411 (2023) at the University of Oslo. We will base the project around the paper: [ZKBS04]. Below follows a list of tasks that needs to be completed for the project.

Project tasks:#

  1. Set up the single-particle basis set.

  2. Create a restricted Hartree-Fock (RHF) ground-state solver.

  3. Compute the RHF ground-state energy, particle density, and dipole moment.

  4. Create a time-dependent restricted Hartree-Fock (TDRHF) solver, and add a time-dependent monochromatic dipole laser-field interaction term to the Hamiltonian.

  5. Compute the time-dependent overlap and the time-dependent dipole moment. Plot the results.

  6. Optional: Run a simulation with a laser pulse, and plot the Fourier spectra of the overlap and the dipole moment after the pulse is turned off.

[CM92]

Daniel T. Colbert and William H. Miller. A novel discrete variable representation for quantum mechanical reactive scattering via the s‐matrix kohn method. The Journal of Chemical Physics, 96(3):1982–1991, 1992. doi:10.1063/1.462100.

[Gri10]

David J Griffiths. Introduction to quantum mechanics. Prentice Hall, second edition, 2010.

[GC93]

Gerrit C. Groenenboom and Daniel T. Colbert. Combining the discrete variable representation with the s‐matrix kohn method for quantum reactive scattering. The Journal of Chemical Physics, 99(12):9681, 1993. doi:10.1063/1.465450.

[JKP09]

C. J. Joachain, N. J. Kylstra, and R. M. Potvliege. Atoms in Intense Laser Fields. Cambridge University Press, 2009. doi:10.1017/cbo9780511993459.

[ZKBS04]

J. Zanghellini, M. Kitzler, T. Brabec, and A. Scrinzi. Testing the multi-configuration time-dependent hartree–fock method. Journal of Physics B: Atomic, Molecular and Optical Physics, 37:763, 2004. doi:10.1088/0953-4075/37/4/004.