Kittel's Solid-State Physics: Deciphering Polarization p

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Homework Help Overview

This discussion revolves around the concept of polarization in the context of solid-state physics, specifically referencing Kittel's textbook. The original poster seeks clarification on the meaning of polarization p as mentioned in relation to normal vibrational modes.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore definitions of polarization and its implications in solid-state physics, questioning the nature of polarization modes and their representation. Some discuss the types of waves in solids and the independence of transverse modes.

Discussion Status

The conversation is ongoing, with participants raising questions about the nature of polarization p and its mathematical representation. There is a mix of definitions and interpretations being explored, but no consensus has been reached yet.

Contextual Notes

Participants note the complexity of polarization modes, suggesting that there may be more modes than integers available for labeling them, which raises questions about the representation of these modes in three-dimensional space.

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Homework Statement


This question refers to Kittel's solid-state physics book.

On this page, Kittel says that "each normal vibrational mode of polarization p has the form of a standing wave." I am not sure what the polarization p refers to?


Homework Equations





The Attempt at a Solution

 
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Well, a wave can be polarised --- solids support longitudinal waves and transverse waves. There will be two independent polarisations for the latter.
 
Can you just define what the polarization of a wave is?
 
http://physics.unl.edu/~tsymbal/tsymbal_files/Teaching/SSP-927/Section%2005_Lattice_Vibrations.pdf

see page 5

etc. just google it
 
Last edited by a moderator:
On Kittel page 109 second sentence, it says "Each normal vibrational mode of polarization p has the form..."

What is "p"?
 
just an integer, n, m, k, l etc.
 
There should be uncountably many polarization modes, which means there are not enough integers to accommodate all of them. There are uncountably transverse directions, aren't there?

Also, do we know what polarization p = 1, for example, corresponds to?
 
No --- there are two independent transverse polarisation modes. The key is the independence. The transverse modes are effectively vectors in a 2D plane.
 
So, a set of polarization modes will always be a basis for \mathbb{R}^3? And you can choose any such basis for your set of polarization modes? So, p will always be 1, 2, or 3?
 
  • #10
anyone?
 
  • #11
anyone?
 
  • #12
Help?
 

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