@misc{9245817,
  abstract     = {{This project concerns the Wannier functions of a two-dimensional electron gas within a simple periodic lattice. Wannier functions are an exponentially localized basis for elec
tron bands and allow for real-space calculations of interacting electron systems. These functions are not unique; using the Wannier functions with minimal spatial spread is the standard in research. In this thesis, the maximally localized Wannier functions were
calculated using a gradient descent algorithm. Wannier functions for a non-interacting system were computed and compared to the equivalent functions computed from an existing density functional theory data set with different electron-electron interaction
strengths. The density function theory Wannier functions showed only minor differences from the non-interacting model. The functions slightly widened, resulting in an 11% increase in the spread for the Wannier function with the strongest Coulomb interaction. The difference observed could be well described as a perturbation of the Wannier
functions scaled by a parameter dependent on the Coulomb strength.}},
  author       = {{Haag, David}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Maximally-localized Wannier functions for a two-dimensional electron gas in a periodic potential}},
  year         = {{2026}},
}