Simulator for a particle in one dimension with periodic boundary conditions
in a timedependent or timeindepend potential by Hanko Ipach and Michael Simon.

We developed this program for the Computational Physics project which is part
of the Bachelor program in Computing in Science at the University of Hamburg.


== HowTo ==

Use the class EVSimulation for a timeindependent potential. This simulation is
computed based on the eigenvectors of it's timeindependent hamilton matrix.

Use StepwiseSimulation for a timedependent potential. This simulation is
computed based on a Crank-Nicolson method with discrete timesteps.


1. Instanciate the classes as described below.
2. Type >sim.plot = true to get the calculation started.
3. Change any parameter and it get's updated in the simulation.
   (Set plot to false to make multiple changes without having to wait until the
    recalculation is done.)
4. Type >sim.new_ev() and >sim.new_stepwise() to clone the simulation to that
   class. Note that StepwiseSimulation instances do not simulate more than one
   step of timedevelopment if the second dimension of V is 1. EVSimulation
   instances on the other hand ignore everything but the first column.


Usage of the classes:

EVSimulation(V, t_max, d_mu, d_sigma, L, k, mass, kin_h_function)
  V               Potential timeindependent -> n x 1       Matrix
                            timedependent   -> n x n_t - 1 Matrix
  t_max           Maximum time to include in the simulation.
  d_mu, d_sigma   Parameters for a normal distribution of the particle.
                  (Use d to specify any distribution.)
  L               Length of simulated space.
  k               k to start with.
  mass            The mass of the particle relative to the electron mass.
  kin_h_function  The function that computes the kinetic hamiltonian.

Everything after t_max can be omitted and is then set to standard values.
StepwiseSimulation has the same usage.