Installation

Dependencies

Schroedinger was build and tested using the following dependency list. Any deviation may result in Schroedinger not working properly

python 3.12+
matplotlib 3.8.2
numpy 2.0.0
scipy 1.12.0
pytest (optional, tests)
build (optional, wheel creation)
sphinx 5.1.1 (optional, documentation)
sphix book theme (optional, documentation)

Compile

To compile schroedinger and generate a wheel package in the dist folder run

python -m build -w

Documentation

Documentation is stored in the docs folder and can be generated by running

cd docs
make html

schrodinger_solve

Solves the one-dimensional, time independent Schroedinger's equation for a given system and generates files with the energies, potential, wave functions and expectation value of the position of the particles. schrodinger_solve takes a file describing the parameters to use and the potential (see below for file format).

Usage

schrodinger_solve [-h] [-o OUTPUT_DIR] filename

Options

positional arguments:
  filename              File describing the system to solve

options:
  -h, --help            show this help message and exit
  -o OUTPUT_DIR, --output-dir OUTPUT_DIR
                        Output directory for the results

Input file format

The input file format consist of a five line header followed by a csv style, two column table describing the potential. Lines in the header that specify multiple parameters are separated by whitespace characters (tab or space). Parameters must be given in a fixed order. Comments discard the rest of the line and may be added with a # character. An empty line is discarded and the next non-empty line specifies the next parameter. A concrete example is given below.

<mass>
<x-min> <x-max> <n-points>
<first-eigenvalue> <last-eigenvalue>
<interpolation-type>
<n>
<x1> <y1>
<x2> <y2>
...
<xn> <yn>

mass: (real) Mass of the particle
x-min, x-max: (real) Solution interval
n-points: (integer) Number of points in the discretization of the solution interval
first-eigenvalue, last-eigenvalue: (integer) Interval of energy eigenvalues to generate

Further examples can be found in the subfolders inside test

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]

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)