I have done several exercises concering periodic potentials in crystal. Especially I did one, where I had to show that the fourier component of the shortest reciprocal lattice vector (call this vector a) in the z-direction was zero. Now solving the problem was just about writing up the right equations (structure factor of basis etc.) But it made me think? What is the physical interpretation of the crystal potentials fourier component of some specific reciprocal lattice vector? And what is the physical interpretation of it vanishing? I also had to show that the fourier component of 2a was not zero, which was not hard. But why is it that this component does not vanish and the component of a does? I don't understand it physically..