Antique.jl

Self-contained, Well-Tested, Well-Documented Analytical Solutions of Quantum Mechanical Equations.

Install

To install this package, run the following code in your Jupyter Notebook:

using Pkg; Pkg.add("Antique")

Usage & Examples

Install Antique.jl for the first use and run using Antique before each use.

using Antique

The energy E(), wavefunction ψ(), potential V() and some other functions are suppoted. Here are examples in hydrogen-like atom. The analytical notation of energy (eigen value of the Hamiltonian) is written as

$$E_n = -\frac{Z^2}{2n^2} E_\mathrm{h}.$$

Hydrogen atom has symbol $\mathrm{H}$ and atomic number 1 ($Z=1$). Therefore the ground state ($n=1$) energy is $-\frac{1}{2} E_\mathrm{h}$.

H = HydrogenAtom(Z=1)
E(H)
# output> -0.5

Helium cation has symbol $\mathrm{He}^+$ and atomic number 2 ($Z=2$). Therefore the ground state ($n=1$) energy is $-2 E_\mathrm{h}$.

He⁺ = HydrogenAtom(Z=2)
E(He⁺)
# output> -2.0

There are more examples on each model page.

Supported Models

• Delta Potential DeltaPotential
• Infinite Potential Well InfinitePotentialWell
• Harmonic Oscillator HarmonicOscillator
• PoschlTeller PoschlTeller
• Morse Potential MorsePotential
• Rigid Rotor RigidRotor
• Infinite PotentialWell 3D InfinitePotentialWell3D
• Spherical Oscillator SphericalOscillator
• Hydrogen Atom HydrogenAtom
• Coulomb 2-Body System CoulombTwoBody

Future Works

List of quantum-mechanical systems with analytical solutions

Developer's Guide

This is the guideline for adding new models. Adding a new model may take from a few days to a week due to reference search, test implementation, and writing documentation.

1. First, please submit a new issue here. We need to find orthodox references (textbooks or papers, not Wikipedia) for the analytical solutions (eigenvalues and eigenfunctions) before the development. This will take more time than you think.
2. Fork the repository on GitHub.
3. Clone the forked repository to your local machine by Git.
4. Please create 3 files:

files	comments
src/ModelName.jl	Write the source codes and docstrings in this file. The most helpful examples are harmonic oscillators for one-dimensional systems and hydrogen atoms for three-dimensional systems. We recommend that you copy these files. First we need to create a structure struct ModelName with the same name as the model name (The best way is Find & Replace). Because the function names conflict, you must always give the struct ModelName as the fisrt argument to V, E, ψ and other functions. Multi-dispatch avoids conflicts. We recommend using Revice.jl while coding. Run include("./developer/revice.jl") on the REPL or use dev.ipynb.
test/ModelName.jl	Write test code in this file. At a minimum, it is recommended to check the normalization and the orthogonality of wavefunction using QuadGK.jl.
docs/src/ModelName.md	Write documnetation in this file. Include at least the definition of the Hamiltonian and the analytical solutions (eigenvalues and eigenfunctions). Calls a docstring in the source code.

5. Please rewrite 5 files:

files	comments
src/Antique.jl	Add the new model name :ModelName to the models = [...] array in this file. : is required at the beginning.
docs/make.jl	Add the new model into pages=[...] in this file.
test/runtests.jl	Change for model in [...] in this file. Please test all models before pull requests.
README.md	Add the new model to the list of supported models.
docs/index.md	Add the new model to the list of supported models.

6. Execute include("./developer/test.jl") to run tests. It will take few minutes to complete.
7. Execute include("./developer/docs.jl") to compile documents. HTML files (docs/build/*.html) will be generated. Please check them with Chrome or any other web browsers.
8. Commit and Push the codes.
9. Submit a pull request on GitHub.

Acknowledgment

Thanks to all contributors. This package was named by @KB-satou and @ultimatile.