Band formation and defects in a finite periodic quantum system

by Todd Timberlake and Neilson Woodfield

This page contains materials to support a journal article submitted to the American Journal of Physics.  The authors have created this page to make available the computational code used to create the figures in the article.  We encourage others to use the code to further explore this simple model system.

• Paper preprint: BandsDefects_TimberlakeWoodfieldv3
• Maxima notebooks (to open and use these notebooks you will need the free, open-source Maxima computer algebra system, available here:wxmaxima-developers.github.io/wxmaxima/ ).  All files are in the form of zip archives and must be extracted before use.
  • Code to find energy eigenvalues for varying number of delta wells (Fig. 2): EvsNplot.wxmx
  • Code to find energy eigenvalues for varying delta well strength (Fig. 5): EvsZplot.wxmx
  • Code to find energy eigenvalues for a strength defect (Fig. 7): EvsZ7defectplot.wxmx
  • Code to find energy eigenvalues for a position defect (Fig. 10): Evsb7defectplot.wxmx
  • Code to plot energy eigenfunctions (Figs. 4, 6, 9, and 12): WavefunctionPlotter.wxmx
  • Code to calculate Bloch bands: BlochTheoryPredictions.wxmx
  • Code to determine existence of zero energy states: ZeroEnergyStates.wxmx
  • Code to read in data files and produce plots: ReadAndPlot.wxmx
• Data files
  • En vs. N (beta=10): EvN9well.txt
  • En vs. beta (N=9): EvZ9well.txt
  • En vs. beta7 (N=9, beta=10 for all but 7): EvZ7defect.txt
  • En vs. b7 (N=9, beta=10): Evb7defect.txt
  • Bloch band limits: BlochBandFiles