A particle confined to an **impassable** **box** is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an** infinite square well** potential. Working with Bill Ditto, Elliott Holliday and I recently explored some of its infinitely many generalizations to two dimensions, including particles confined to regions that exhibit **integrable**, **ergodic**, or **chaotic** classical billiard dynamics, using **physics-informed neural networks**. In particular, we generalized an **unsupervised learning algorithm** to find the particles’ **eigenvalues** and **eigenfunctions**, even in cases where the eigenvalues are **degenerate**. During training, the neural network adjusts its **weights** and **biases**, one of which is the energy eigenvalue, so that its output approximately solves the **stationary Schrödinger equation** with **normalized** and **mutually orthogonal** eigenfunctions.

# Neural network does quantum mechanics

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Nice post, John! Thanks for writing these. I always enjoy them.

David Smith’s ein stein is an awesome shape!

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Thanks, Mark! I enjoy reading your posts as well.