Register to reply

Question about Bloch function in Reduced Zone Scheme

by ck00
Tags: bloch, function, reduced, scheme, zone
Share this thread:
ck00
#1
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?
Phys.Org News Partner Physics news on Phys.org
'Squid skin' metamaterials project yields vivid color display
Scientists control surface tension to manipulate liquid metals (w/ Video)
Simulation method identifies materials for better batteries
0xDEADBEEF
#2
Jan12-13, 02:06 PM
P: 825
He probably defines [itex]u_k(r)[/itex] this way. It is just the old u times a complex phase.


Register to reply

Related Discussions
Bloch function of an infinite, 1-D linear chain of dz2 orbitals. Advanced Physics Homework 0
Help for supercell, Bloch function Atomic, Solid State, Comp. Physics 2
Reduced zone scheme Atomic, Solid State, Comp. Physics 2
Bloch function - Solid state physics Advanced Physics Homework 0
How would the human body function at reduced sizes? Biology 16