QLine 1.2

For the calculation of one-dimensional Schroedinger equations

QuantumLine(QLine)

Quantumline (QLine) is a python package for solving one-dimensional Schroedinger equations using the variational principle and to plot the results in a comfortable way.

QLine lives on gitlab (https://gitlab.com/micwe/qline).

The documentation can be found on the corresponding gitlab pages:

https://micwe.gitlab.io/qline/

Installation

Just execute:

pip install qline

Usage

See examples directory for some examples of typical runs.

QLines can be run using Python's interpreter, or interactively with some of the interactive Python consoles.

Example: Harmonic Potential

The theoretical background can be found in the following PDF:

# import QuantumLine package
import QLine as ql
# import numpy standard package
import numpy as np

# Creating a linear Grid
grid = ql.Grid()
x = grid.create_linear_grid()
grid.show_attributes(show=True)

# Create a potential function V(x) (harmonic oscillator)
pot = ql.harmonic_potential(x)

# Configure basis set method (variational principle) 
# For solving Schroedinger equation
N = 10 # Size of basis set

# Run basis set method
# lamb = eigenvalues
# coeff = basis function coefficients (for wave functions)
# basis = basis functions
lamb, coeff, basis = ql.basis_set_method(x, pot, N=N)

print("\n\nEigenenergies:\n", lamb)
print("\n\n(Function) Coefficients:\n", np.around(coeff.real,decimals=2))

# Construct eigenfunctions (wave functions) 
# by combining coefficients and basis functions
wf = ql.wave_function_from_coeff(coeff, basis)

# Visualize wave functions within potential function
# on the associated energies
ql.plot_wfunctions_within_potential(x, pot, lamb, wf,
                                    xmin=-8, xmax=8,
                                    ymin=-0.3, ymax=10.5,
                                    savefig=False)

# Visualize energy level diagram
ql.plot_energy_levels(lamb, savefig=False)