Lecture 26. january 1999

We mentioned

what role do the eigenmodes have. How to excite an
eigenmode. (linear equations -> superposition)

We mentioned the 'resonances' - they are excitations 
of eigenmodes.

The string with a basis. Derivation of the equations.

..... In the lecture a mistake - 'a' was supposed to be
      the distance between the atoms m1 and m2. In the
      standard derivation 'a' is the length of the cell,
      i.e. from m1 to m1. 

      Acoustical branch and optical branch. Origin of the
      names.

As omega goes to zero:

Density of modes in one-dimensional space (constant) 
Density of modes in two-dimensional space (prop. to omega)    
Density of modes in three-dimensional space (prop. to omega*omega)

Solutions in two and three dim. space.
vector displacement
vector wave number
the modes have 'polarization vectors'
The equations become only more complicated, in principle
the same method.