Kronig-Penney model of a 1-D periodic potential and resulting dispersion and density-of-states curves 

Program to plot the dispersion curve and density of states of a 1-D array of atoms according to the Kronig-Penney model, a simplified model in solid-state physics for electrons in a one-dimensional pulselike periodic potential. See for example https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice for the physics background. 

The program allows the user to vary one of three parameters - the height of the rectangular potential representing the ionic cores; the periodicity of the 1-D array; and the duty cycle of the array, i.e., the ratio of the width of the rectangular pulse to the periodicity. Three examples are provided. 

Download mp4 

animation 

Download mp4 

animation 

Download mp4 

animation