Dispersion on a chain of atoms
Take 15 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
If you have more questions, feel free to ask them on the forum.
Why doesn't depend on ?
The wave is neither stationary nor damped : all atoms are therefore the same amplitude for a progressive wave.
The system is generally translational invariant.
Thus, is independent of the considered atom.
Determining, as a function of , the possible values of the wave frequency that can propagate on the chain.
What does we deduce from the nonlinearity of this relationship ?
Calculate the phase and group velocities .
Give their limits for and and comment.