SAIP2026

Physics-Informed Neural Networks for two-Body Schrödinger Bound-State Eigenvalue Computation

8 Jul 2026, 10:10

20m

Lecture Hall DL2 (University of the Western Cape)

Oral Presentation Track G - Theoretical and Computational Physics Theoretical and Computational Physics

Speakers

Dr Tshegofatso Tshipi (Sol Plaatje University)Dr Ishmael Gopane (Sol Plaatje University)

Description

We have previously shown that unsupervised Physics‑Informed Neural Networks can give promising results for quantum few‑body problems, where we computed the s‑wave bound states generated by a toy potential and the Woods–Saxon potential. The method performed well for the toy potential, but it struggled to learn the second excited state of the Woods–Saxon potential. This difficulty arose because the neural network introduces unphysical constraints in the loss function for the eigenvalue–eigenfunction pairs during training. In this work, we improve the method by using the known properties of Hermitian operators, in particular, that the bound‑state eigenfunctions are normalized and orthonormal. Using these properties, the bound‑state energies are approximated with the Rayleigh–Ritz variational method, and the corresponding physical constraints are included directly in the loss function. The performance of the approach is tested on a toy potential, the  Gaussian type potential, and the Woods–Saxon potential. Preliminary results show that including these physical constraints in the loss function improves the accuracy and stability of the neural network solutions, especially for excited states.