A real-time solver for Schrödinger's equation in 2D, focusing on the particle in a box problem.
On the graphical side of the project, the idea is to use an eigenvalue/eigenstate representation of the quantum mechanical system. In this way we can avoid solving any differential equations in the graphical software and instead reconstruct solutions from known eigenstates. This process can be done entirely as graphics shaders, allowing the software to run on low power devices.
On the backend side of the project, for a given potential the energy eigenvalues and eigenstates need to be precomputed. Applying a Wick rotation to the Schrödinger equation produces a new equation that is analogous to the diffusion equation with an added source term. The energy eigenstates can be found from this equation using a Gram-Schmidt orthonormalization.