
#1
Jan1213, 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? 



#2
Jan1213, 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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