Joined: June 2006
On page 99 of Quantum Physics (Gasiorowicz):
The Hamiltonian is invariant under displacements of 'a' (the period)
E = hbar^2*k^2/2m
Here, the periodicity of the universe is around 300 Mpc (homogeneity), tell me how you apply any sort of band structure when the perodicity of the universe so large. Take your time. Even in natural units, comparing this to an insulator/conductor makes no sense. Particularly when the value of a increases (and E), the band structure is non-existant (using the approximation <sigma-x> << a). If you need assistance with the math, I'm always here to help.