I am asked to simulate the first two eigenvectors for a periodic potential V(x)=V0cos(x). I have attached those two (blue is first, green is second). And I am then asked to explain why they look the way they do. I wrote: Because a particle needs to tunnel through a lot of potential barriers to reach high and low x values it is natural that we see the wave function decreasing symmetrically about x=0. However I am not quite sure of this - does anyone think it sounds reasonable?