Why Use Reciprocal Lattice for Band Structure?

[new_986]

Reciprocal lattice?

Hi everybody...
I'm read about the band structure and the dispersion curve,I've got informations about the reciprocal lattice and how we determine it, but what I want to know why we use the reciprocal lattice in band structure calculations?

thanks

 

[vkroom]

because most lattices are translation invariant, momentum is a "good" quantum number, i.e. it is conserved. this leads to a diagonal representation of all other conserved quantities in the momentum space, which is especially simple to work with.