Speaker
Description
Physics-Informed Neural Networks (PINNs) provide a flexible framework for solving differential equations by embedding the governing physical laws directly into the training process. In this work, we investigate the use of PINNs for the solution of the three-dimensional time-independent Schrödinger equation in spherical coordinates, focusing on nuclear single-particle states described by Woods–Saxon type potentials.
The proposed approach is based on a separable representation of the wavefunction in radial and angular components. The nuclear mean-field potential includes the central Woods–Saxon term, the spin–orbit interaction, and the isospin-dependent Lane contribution. This allows the method to describe neutron and proton single-particle states in representative doubly-magic nuclei, including 16O, 40Ca, 48Ca, and 56Ni.
The PINN is trained by minimizing a composite physics-informed loss function that combines the Schrödinger equation residual, boundary conditions, normalization constraints, energy minimization, and orthogonality conditions for excited states. The computed energy spectra and probability densities are compared against an independently developed finite-difference solver and reference single-particle spectra from the literature.
The results show that the PINN framework accurately reproduces bound-state energy levels, preserves the correct level ordering, and captures characteristic nuclear-structure features such as spin–orbit splittings. The learned radial probability densities exhibit physically consistent localization inside the nuclear region and exponential decay at large distances. Although the PINN approach is computationally more demanding than the finite-difference baseline, it offers a continuous, differentiable, and physics-consistent representation of the nuclear wavefunction.
Overall, this work demonstrates that Physics-Informed Neural Networks can provide a promising alternative numerical framework for nuclear Schrödinger eigenvalue problems and may serve as a basis for future extensions toward inverse problems, parameter estimation, and more complex nuclear mean-field models.