Deriving the Phonon Dispersion Relation using Quantum-mechanical approach

[mosqui]

I'm doing a literature review on dispersion relations, and I've been told that if i can derive the phonon dispersion relation, it would help my review. So i was wondering if anybody could help me with the derivation either through Quantum-mechanical approach or Semi-classical treatment of lattice vibrations. Any reference or extra guidance would be sincerely appreciated.

 

[daveyrocket]

Ashcroft and Mermin has a nice chapter on it.

 

[mosqui]

okay, thanks.. but do you have a soft copy of the book or a link where i can get it from. pleeeeeeeeaaaaaaaaase.

 

[ZapperZ]

This is a copyrighted book and free distribution of it is illegal and violates the rules of this forum.

This is a common topic covered in intro Solid State Physics text. If you need to do it, then you need to find such a text.

Zz.

 

[mosqui]

oops.. Sorry i didn't know.

 

[mosqui]

but can you help me out with an idea or something about the proof, because purchasing that book is kinda troublesome.

 

[nasu]

Wikipedia has a quite detailed article on this topic.
Search (Google) "Phonon dispersion relations" and you'll find many detailed pages.

 

[daveyrocket]

You don't have access to a library?

 

[mosqui]

@nasu, your link to Wikipedia was very helpful, and I'm very grateful. But i was hoping you could assist me again with another project. It is the derivation of the phonon dispersion relation using classical and quantum treatment in 1d, 2d and 3d. Please any help will be sincerely appreciated, thank you