README.md

Interactive Notebooks: Quantum Mechanics and Computational Materials Science

Introduction

This is a repository for tutorials in quantum mechanics and computational materials science. Jupyter notebooks are converted into interactive web applications. Professors can use them to demonstrate knowledge in the classroom. Students can also use them for self-learning.

• Try on Materials Cloud (fast, a few seconds to load)

• Try on BinderHub (can take > 1 minute to load)

Local installation

One can clone this repository and install all the required packages locally. To do so (ideally in a fresh python virtual environment, to reduce risks of version clashes of some of the dependencies), run the following commands:

git clone https://github.com/osscar-org/quantum-mechanics.git
cd quantum-mechanics
pip install -r requirements.txt

Then, to view the notebooks in the form of a web application, you can type the following command in the terminal:

voila --template=osscar --VoilaConfiguration.enable_nbextensions=True notebook/

This will start the voila server and then open your default browser, where you can use the web application.

Content

Section 1: Quantum Mechanics

Here are the tutorials to demonstrate numerical solution for 1D Schrödinger equation.

Name	Description	Notebook links	Binder	Materials Cloud
One Quantum Well	The solution for 1 quantum well	One Quantum Well
Two Quantum Wells	The solution for 2 quantum wells	Two Quantum Wells
Asymmetric Well	Avoided crossing in an asymmetric well	Asymmetric Well
Shooting method	Shooting method with Numerov algorithm	Shooting method
SOFT	Split operator Fourier transform method	SOFT
MSOFT	Multiple Split operator Fourier transform method	SOFT

Section 2: Band Theory of Crystals

Here are the tutorials to demonstrate the band theory of crystal systems.

Name	Description	Notebook links	Binder	Materials Cloud
FFT and Planewaves	Fourier Transforms and Plane-Wave Expansions	FFT and Planewaves
Free Electron	Free-electron Bands in a Periodic Lattice	Free Electron
Density of States	Density of States (DOS)	Density of States
Pseudopotentials	Norm-conserving pseudopotentials	Pseudopotentials
Brillouin Zone	Brillouin Zone	Brillouin Zone

Section 3: Molecule and Lattice Vibration

Name	Description	Notebook links	Binder	Materials Cloud
Phonon 1D	lattice vibration for one dimensional system	Phonons 1D
Phonon 2D	lattice vibration for two dimensional systems	Phonon 2D
Molecular Vibrations	introduce to molecular vibrations	Molecular Vibration

Section 4: Molecular Dynamics

Name	Description	Notebook links	Binder	Materials Cloud
Verlet Integration	Verlet integration	Verlet Integration

Section 5: Statistical Mechanics

Name	Description	Notebook links	Binder	Materials Cloud
Metropolis Monte Carlo	Metropolis-Hastings Monte Carlo	Metropolis Monte Carlo
Monte Carlo Integration	Monte Carlo Integration	Monte Carlo Integration
Ising Model	Ising Model	Ising Model

How to contribute

If you would like to contribute a new notebook to OSSCAR, see the guide to contributing on our website, where you can also find an example notebook template.

How to cite

When using the content of this repository, please cite the following article:

D. Du, T. Baird, S. Bonella and G. Pizzi, OSSCAR, an open platform for collaborative development of computational tools for education in science, Computer Physics Communications, 282, 108546 (2023). https://doi.org/10.1016/j.cpc.2022.108546

Acknowledgements

We acknowledge support from the EPFL Open Science Fund via the OSSCAR project.