This simulation works by approximating the position space Hamiltonian H of the quantum system using a uniform finite difference grid, where its energy eigenstates |n> and eigenvalues Eₙ are subsequently solved for. From here this numerically-approximated quantum system's wave function |ψ> is expressed as a linear combination of its energy eigenstates |n>, where

Here t is the time elapsed in the simulation, and the cₙ(t) are complex-valued coefficients, where they are visually represented using circular "clock face" sliders that can be interactively modified in real time by the user. The lengths of these circular sliders are proportional to |cₙ(t)|, and their angular offsets are determined by their phase factors arg(cₙ) - Eₙt/ħ.

The UI and visual style of this interactive simulation are based on Paul Falstad's various quantum mechanics apps. An additional inspiration are Daniel Schroeder's many quantum mechanics programs. Computations for obtaining the eigenvectors and eigenvalues of the numerically approximated Hamiltonian matrix are found using Eigen and Spectra. Both are licensed under the MPL2.