Register to reply

Proof of Blochs function.

by silverwhale
Tags: blochs, function, proof
Share this thread:
Oct4-13, 05:08 AM
P: 67
Hi Everybody,

I am learning solid state physics and read today through Kittel. I am still stuck at the proof of Blochs theorem i.e. the proof of Blochs function.

For the Schrodinger equation of a periodic potential the general ansatz:

[tex] \psi = \sum_k C_k e^{ikr} [/tex]

is made.

Then, by looking at the Schrodinger equation in the reciprocal lattice, we see that the [itex] C_k [/itex] are a linear combination of [itex] C_{k-G} [/itex], where [itex]G[/itex] is the reciprocal lattice vector.

Finally, the wave function is indexed by an index [itex] k [/itex] and rewritten as:

[tex] \psi_k = \sum_G C_{k-G} e^{i(k-G)r}, [/tex]

where the sum goes now over G.

I have two questions:
1) How can we go from the sum over k to a sum over G?
2) Is [itex] \psi_k [/itex] the same function as [itex] \psi [/itex]? If so, why do we index it with k?

I hope this is clear enough, and I would be glad for ANY answer!! :)
I am searching for an ansatz for nearly a week now!!
Phys.Org News Partner Physics news on
New complex oxides could advance memory devices
'Squid skin' metamaterials project yields vivid color display
Scientists control surface tension to manipulate liquid metals (w/ Video)

Register to reply

Related Discussions
Proof about phi function Calculus & Beyond Homework 1
Blochs theorem Quantum Physics 0
Set function proof Set Theory, Logic, Probability, Statistics 11
Function Proof . . . Precalculus Mathematics Homework 2
Proof of function General Math 4