Kittel's Solid-State Physics: Deciphering Polarization p

[ehrenfest]

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

 

[genneth]

Well, a wave can be polarised --- solids support longitudinal waves and transverse waves. There will be two independent polarisations for the latter.

 

[ehrenfest]

Can you just define what the polarization of a wave is?

 

[malawi_glenn]

http://physics.unl.edu/~tsymbal/tsymbal_files/Teaching/SSP-927/Section%2005_Lattice_Vibrations.pdf

see page 5

etc. just google it

 

[ehrenfest]

On Kittel page 109 second sentence, it says "Each normal vibrational mode of polarization p has the form..."

What is "p"?

 

[malawi_glenn]

just an integer, n, m, k, l etc.

 

[ehrenfest]

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?

 

[genneth]

No --- there are two independent transverse polarisation modes. The key is the independence. The transverse modes are effectively vectors in a 2D plane.

 

[ehrenfest]

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?

 

[ehrenfest]

anyone?

 

[ehrenfest]

anyone?

 

[ehrenfest]

Help?