Use the force
--------------------


    * **Topic:** atomistic models, pair potentials, conservative forces 
    * **Task:** 
        1. Implement the method that calculates forces on all atoms.
        2. Run the program and compare your forces against values the
           program calculates by numerically differentiating the potential energy.
           If your function works, *all* values should be a close match.
           If there are *any* notable discrepancies, there is a bug.
        3. Change the :math:`\Delta` parameter and study how it affects
           numeric accuracy. Does the numeric result approach your analytic solution?
        4. Make the program create random configurations
           and check that you always get matching results.        
    * **Template:** `forces.py <http://users.utu.fi/tejohy/teaching/simu/templates/forces.py>`_
    * **Data:** `atoms.txt <http://users.utu.fi/tejohy/teaching/simu/templates/atoms.txt>`_
    * **Further reading:**
        - https://en.wikipedia.org/wiki/Conservative_force
        - https://en.wikipedia.org/wiki/Lennard-Jones_potential
        

forces.py
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.. automodule:: forces
    :members:
    :undoc-members: