Infinite square well 📦

About

The infinite square well is also known as the infinite potential well or the infinite square well.

A 2D Infinite Square Well (ISW) is a potential well that has zero potential energy over a finite domain in two directions, say the $x$- and $y$-directions, and is infinite outside that domain. The simplest case is a rectangular domain in the $xy$-plane with sides $L_x$ and $L_y$. In this case the 2D time-independent Schrödinger wave equation factors into two 1D time-independent Schrödinger wave equations, one in the $x$-direction and one in the $y$-direction. The wavefunction is then a product of the two 1D wavefunctions. The wavefunction is then given by a superposition of energy eigenstate wavefunctions of the form $\psi_{nm}(x, y) = A \sin(n\pi x/L_x) \sin(n\pi y/L_y )$. — Visualizing Quantum Mechanics with Python

A 2D square well visualized in 3D

🧠 Idea taken from the book Visualizing Quantum Mechanics with Python
📌 Highly recommended background information: Visualizing complex numbers and wavefunctions in one and two dimensions