# Question about Bloch function in Reduced Zone Scheme

1. Jan 12, 2013

### ck00

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?

Last edited: Jan 12, 2013
2. Jan 12, 2013

He probably defines $u_k(r)$ this way. It is just the old u times a complex phase.