A is some constant, and a is the lattice constant (the spacing between each site). Since this potential is periodic, we could expand it as a Fourier series: V ( x ) = ∑ ∑ K V ~ ~ ( K ) ⋅ ⋅ e i K x , where V ~ ~ ( K ) = 1 a ∫ ∫ − − a / 2 a / 2 d x V ( x ) e − − i K x = 1 a ∫ ∫ − − a / 2 a / 2 d x ∑ ∑ n = − − ∞ ∞ ∞ ∞ A ⋅ ⋅ δ δ ( x − − n a ) e − − i K x = A a .