The Variational Principle in Quantum Mechanics states that:
This implementation utilises NumPy and Matplotlib to numerically calculate the energy eigenstates and energy eigenvalues of the given bounded potential system.
The code is capable of calculating the bound energies and states of any number of energy eigenstates, with decreasing accuracy with each new state.
The code can handle systems of any number of dimensions, but can only plot the energy eigenstates of a system up to and including 3D.
For full details read
First, setup a virtualenvironment and install the requirements:
$ python -m virtualenv venv$ source venv/bin/activate$ pip install -r requirements.txtEnsure the setup steps above are run.
From the top level directory:
$ python -m variational_principle.mainShould result in a help message like the following:
main.py - A tool to calculate the n energy eigenstates for a given bound potential
USAGE:
main.py [FLAGS] <start> <stop> <N>
FLAGS:
-i/--include-potential Whether or not to plot the calculated graphs with the given potential superimposed
(default = False)
-v/--v-scale Scaling factor used on the potential when --include-potential is True (default = 10)
-d/--dimensions The number of dimensions to calculate on, options are 1, 2 or 3 (default = 1)
-n/--num-states Number of energy eigenstates to calculate (default = 1)
-n/--num-iterations The number of iterations to calculate (default = 10^5)
-h/--help Show this message
ARGUMENTS:
<start> The initial coordinate for the grid
<stop> The end coordinate for the grid
<N> The number of subdivisions of the gridTo verify the code will run correctly, the easiest input is:
$ python -m variational_principle.main -1 1 1If no errors occur, a GUI should appear with an empty plot.
After that, happy plotting!
Using pyinstaller an executable binary can be compiled:
$ pyinstaller --onefile binary.specWill compile an executable binary at dist/variational_principle.
Run the binary as usual with
$ ./dist/variational_principle [...input]
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