Deriving the Phonon Dispersion Relation using Quantum-mechanical approach

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Discussion Overview

The discussion revolves around deriving the phonon dispersion relation using quantum-mechanical and semi-classical approaches. Participants seek guidance, references, and ideas related to this topic, which is relevant in the context of solid-state physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant is conducting a literature review on dispersion relations and seeks help with deriving the phonon dispersion relation.
  • Another participant suggests that Ashcroft and Mermin's book contains a relevant chapter on the topic.
  • A request for a soft copy of the book is made, highlighting the difficulty of purchasing it.
  • A participant reminds others that sharing copyrighted material is against forum rules.
  • There is a suggestion to consult introductory solid-state physics texts for guidance on the derivation.
  • One participant points out that Wikipedia has a detailed article on phonon dispersion relations, which could be useful.
  • A follow-up request for assistance with the derivation in different dimensions (1D, 2D, and 3D) is made, indicating a desire for further help beyond the initial inquiry.

Areas of Agreement / Disagreement

Participants generally agree on the importance of established texts and resources for understanding the phonon dispersion relation, but there is no consensus on the best approach or specific resources to use. The discussion remains unresolved regarding the derivation methods.

Contextual Notes

Participants express uncertainty about accessing resources and the legality of sharing copyrighted materials, which may limit their ability to obtain necessary references for the derivation.

Who May Find This Useful

Readers interested in solid-state physics, phonon dispersion relations, and those seeking resources for academic projects may find this discussion relevant.

mosqui
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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.
 
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Ashcroft and Mermin has a nice chapter on it.
 
okay, thanks.. but do you have a soft copy of the book or a link where i can get it from. pleeeeeeeeaaaaaaaaase.
 
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.
 
oops.. Sorry i didn't know.
 
but can you help me out with an idea or something about the proof, because purchasing that book is kinda troublesome.
 
Wikipedia has a quite detailed article on this topic.
Search (Google) "Phonon dispersion relations" and you'll find many detailed pages.
 
You don't have access to a library?
 
@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
 

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