Computing the Density of States and Energy Bands of a 1-Dimensional Lattice Using Transfer Matrices

The Kronig-Penney model is typically used to compute the band structure and bound states of a periodic crystal. While the model allows analytical solutions, it does so by simplifying the potential to a periodic square potential. We present a method of using transfer matrices to compute energy bands in a 1-Dimensional lattice. This method does not involve the simplification required by the Kronig-Penney model and has the advantage of being able to model ’real’ potentials.