# Kittel page 109

1. Mar 21, 2008

### ehrenfest

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. The attempt at a solution

2. Mar 21, 2008

### genneth

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

3. Mar 22, 2008

### ehrenfest

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

4. Mar 22, 2008

### malawi_glenn

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

see page 5

Last edited by a moderator: May 3, 2017
5. Mar 24, 2008

### ehrenfest

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

What is "p"?

6. Mar 24, 2008

### malawi_glenn

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

7. Mar 24, 2008

### 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?

8. Mar 24, 2008

### genneth

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

9. Mar 24, 2008

### 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?

10. Mar 25, 2008

### ehrenfest

anyone?

11. Mar 26, 2008

### ehrenfest

anyone?

12. Mar 26, 2008

Help?