*****************
Schrodinger Plot
*****************

Plots the solutions of schrodinger_solve. Visualises the given potential together
with the eigenstates and the probability density. Also plots the standard
deviation of each energy level.

Solutions of schrodinger_solve must be in a directory together for schrodinger_plot
to visualise them. Solution files must keep names given by schrodinger_solve.

The plot generated by schrodinger_plot can be altered with different scale and
axis limits to better visualize the solution. If no custom scale or limits are given
schrodinger_solve will limit the plot by the limits of the potential as well as the
energies of the solution for a better initial result.

**Usage**
::

   schrodinger_plot.py [-h] [-s SOLUTION_DIR] [-o OUTPUT_DIR] [--show SHOW] [-e EXPORT] [--scale SCALE] [-x XLIM] [-y1 ENERGY_LIM] [-y2 UNCERTAINTY_LIM]

**Command line options**
::

  -h, --help            show a help message
  -s SOLUTION_DIR --solution_dir
                        the path of the solution directory (default: None)
  -o OUTPUT_DIR --output_dir
                        the path where the pdf should be saved (default: None)
  --show SHOW           Boolean, if True the plot is shown directly (default:
                        True)
  -e EXPORT --export
                        Boolean, if True the plot is exported as a pdf
                        (default: True)
  --scale SCALE         Float, scales the wave functions (default: 1.0)
  -x XLIM --xlim        Limit of the x-axis of the left plot. None or
                        tuple[float, float] of shape (x_min, x_max)(default:
                        None)
  -y1 ENERGY_LIM --energy_lim
                        Limit of the y-axis of the left plot. None or
                        tuple[float, float] of shape (y_min, y_max)(default:
                        None)
  -y2 UNCERTAINTY_LIM --uncertainty_lim
                        Limit of the y-axis of the right plot. None or
                        tuple[float, float] of shape (y_min, y_max)(default:
                        None)