Hi, I'm trying to understand the bound states of a periodic potential well in one dimension, as the title suggests. Suppose I have the following potential, V(x) = -A*(cos(w*x)-1). I'm trying to figure out what sort of bound energy eigenstates you'd expect for a potential like this. Specifically would the wave-functions for these bound energy eigenstates be periodic. I chose this potential because it looks sort of like a harmonic oscillator's potential about x = 0. So would the lowest bound state look like the harmonic oscillators ground state except periodic? Or would it look like the harmonic oscillators ground state while dying off and not being periodic?