I Understanding r^t & a: Seeking Clarification on Raman Spectra

[chobo]

Hi all, I am studying in Raman spectra and I don't know
that what's means r^t a r =1.
r^t is r transpose, r^t=(x,y,z).
And a is diagonalized polarizability tensor.
Whats means that is equal 1?
Just normailzation?
Help me,and so sorry my english is too bad...

 

[chobo]

ref is
Spectra of atoms and molecules
Peter F. Bernath
ch.8

 

[DrClaude]

It is simply the equation for an ellipsoid, see http://mathworld.wolfram.com/Ellipsoid.html

 

[chobo]

Dr Claude/
Just defined ellipsoid? That is all?
I mean, what is Matmatical process that's eq.

 

[DrClaude]

The vector notation is just a shorthand. If you expand the vector-matrix-vector product, you will see that what you get is the equation for an ellipsoid, with the elements of the polarizability tensor determining the size and shape of the ellipsoid. This is clearest when the polarizability is diagonal, as seen in the book. The point of all this is to get a visual representation of the polarizability.