# The relation between spectral function and band structure

I am confused by the wavevector in spectral function $A(\mathbf k,\omega)$. How to understand this $\mathbf k$ for a periodic structure? And how is it related to the $\mathbf k$ (in first Brillouin Zone) we use in the band structure? If there are multibands, then in band structure for the same k we have several energies. To roughly reproduce spectral function, do I expect several peaks for the same $\mathbf k$ in $A(\mathbf k,\omega)$ or I need to unfold the multibands, and the multi energies for same $\mathbf k$ in band structure appear at different $\mathbf k$ in $A(\mathbf k,\omega)$?

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You should try to do the calculation for free electrons for a two-band model and see what happens (and tell us the resul !). – Adam Apr 15 '14 at 0:54