Harmonic1DMD:Background:Harmonic 1DMD Analytical Solution
An analytical solution has been developed that describes Lattice Vibrations of 1D
atom chains. The solution comes in the form:
where is displacement from position na at time t.
This equation can then be rewritten as:
From this you can find the displacement of any atom, at position na and at time t, given k and .
By setting the proper conditions (periodic boundary), and assuming harmonic
interactions (like springs), k and become the following: