Question about Bloch function in Reduced Zone Scheme

by ck00
Tags: bloch, function, reduced, scheme, zone
ck00 is offline
Jan12-13, 01:26 AM
P: 19
The classical textbook, Introduction to solid state physics by Charles Kittle said:
"If we encounter a Bloch function written as [tex]ψ_{k’}(r)=exp(i{k’}r) u_{k’}(r)[/tex], 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
[tex]ψ_{k’}(r)=exp(ik’r) u_{k’}(r)=exp(ikr) [exp(-iGr) u_{k’}(r)][/tex]
[tex]=exp(ikr) u_k(r)=ψ_k(r)[/tex]"
I wonder why [tex]exp(-iGr) u_{k’}(r)=u_k(r)[/tex], how to derive this relation?
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0xDEADBEEF is offline
Jan12-13, 02:06 PM
P: 824
He probably defines [itex]u_k(r)[/itex] this way. It is just the old u times a complex phase.

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