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

using Antique
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

InfinitePotentialWell InfinitePotentialWell
HarmonicOscillator HarmonicOscillator
PoschlTeller PoschlTeller
MorsePotential MorsePotential

Future Works

List of quantum-mechanical systems with analytical solutions

Developer's Guide

Here is the guideline for adding new models.

Acknowledgment

This package was named by @KB-satou and @ultimatile.