# Question about Bloch function in Reduced Zone Scheme

by ck00
Tags: bloch, function, reduced, scheme, zone
 P: 19 The classical textbook, Introduction to solid state physics by Charles Kittle said: "If we encounter a Bloch function written as $$ψ_{k’}(r)=exp(i{k’}r) u_{k’}(r)$$, with k’ outside the first zone, we may find a suitable reciprocal lattice vector G such that k=k’+G lies within the first Brillouin zone. Then $$ψ_{k’}(r)=exp(ik’r) u_{k’}(r)=exp(ikr) [exp(-iGr) u_{k’}(r)]$$ $$=exp(ikr) u_k(r)=ψ_k(r)$$" I wonder why $$exp(-iGr) u_{k’}(r)=u_k(r)$$, how to derive this relation?
 P: 827 He probably defines $u_k(r)$ this way. It is just the old u times a complex phase.

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