Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

https://github.com/ohno/Antique.jl

Self-contained, Well-Tested, Well-Documented Analytical Solutions of Quantum Mechanical Equations
https://github.com/ohno/Antique.jl

chemistry julia physics quantum-mechanics

Last synced: 27 days ago
JSON representation

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

Lists

README 

        
# Antique.jl



[![Build Status](https://github.com/ohno/Antique.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/ohno/Antique.jl/actions/workflows/CI.yml?query=branch%3Amain) 

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://ohno.github.io/Antique.jl/stable/)

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://ohno.github.io/Antique.jl/dev/)



Self-contained, Well-Tested, Well-Documented **An**aly**ti**cal Solutions of **Qu**antum Mechanical **E**quations.



## Install



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



```julia

using Pkg; Pkg.add("Antique")

```



## Usage & Examples



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



```julia

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



```math

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 $-\frac{1}{2} E_\mathrm{h}$.



```julia

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 $-2 E_\mathrm{h}$.



```julia

He⁺ = HydrogenAtom(Z=2)

E(He⁺)

# output> -2.0

```



There are more examples on each model page.



## Supported Models



- [Delta Potential](https://ohno.github.io/Antique.jl/stable/DeltaPotential/) `DeltaPotential`

- [Infinite Potential Well](https://ohno.github.io/Antique.jl/stable/InfinitePotentialWell/) `InfinitePotentialWell`

- [Harmonic Oscillator](https://ohno.github.io/Antique.jl/stable/HarmonicOscillator/) `HarmonicOscillator`

- [PoschlTeller](https://ohno.github.io/Antique.jl/stable/PoschlTeller/) `PoschlTeller`

- [Morse Potential](https://ohno.github.io/Antique.jl/stable/MorsePotential/) `MorsePotential`

- [Rigid Rotor](https://ohno.github.io/Antique.jl/stable/RigidRotor/) `RigidRotor`

- [Infinite PotentialWell 3D](https://ohno.github.io/Antique.jl/stable/InfinitePotentialWell3D/) `InfinitePotentialWell3D`

- [Spherical Oscillator](https://ohno.github.io/Antique.jl/stable/SphericalOscillator/) `SphericalOscillator`

- [Hydrogen Atom](https://ohno.github.io/Antique.jl/stable/HydrogenAtom/) `HydrogenAtom`

- [Coulomb 2-Body System](https://ohno.github.io/Antique.jl/stable/HydrogenAtom/) `CoulombTwoBody`



## Future Works



[List of quantum-mechanical systems with analytical solutions](https://en.wikipedia.org/wiki/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 or or comment [here](https://github.com/ohno/Antique.jl/issues). I will assign you to the issue. 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](https://github.com/ohno/Antique.jl) 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, please check the normalization and the orthogonality of eigenfunction using QuadGK.jl. Please also do tests for eigenvalue (for example, calculate the expectation values of the Hamiltonian (energy) using the eigenfunctions and check that these values match the eigenvalues). |

| `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 (`src/ModelName.jl`) . |



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](https://github.com/KB-satou) and [@ultimatile](https://github.com/ultimatile).