Physics informed machine learning architectures for the solution of fundamental quantum mechanics equations
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Keywords
PINNs ; TISE ; TDSE ; Machine learning ; AI ; Woods Saxon ; 3D ; Nuclear ; QuantumAbstract
This thesis investigates the use of Physics-Informed Neural Networks (PINNs) as a unified
framework for solving fundamental equations of quantum mechanics. The main objective is
to assess their ability to approximate solutions of both time-dependent and time-independent
Schrödinger equations while enforcing physical constraints directly through the loss function. The
methodology is first validated on the one-dimensional time-dependent Schrödinger equation for
the quantum harmonic oscillator, where PINNs accurately reproduce the evolution of superposed
quantum states while preserving normalization and stability. The approach is then extended to
time-independent problems using a variational formulation that combines energy minimization
with orthogonality constraints, enabling the computation of both ground and excited states. A
structured PINN framework is further developed for three-dimensional problems using separation
of variables in spherical coordinates. The method is validated against analytical solutions of
the harmonic oscillator, demonstrating high accuracy in eigenvalues and probability densities.
Finally, the framework is applied to realistic nuclear physics problems using the Woods–Saxon
mean-field potential. The results are validated through comparisons with literature, analytical
solutions and finite-difference method, showing that PINNs can recover physically meaningful
solutions across different problem settings. Overall, the study demonstrates that PINNs provide
a flexible and physics-consistent alternative to traditional numerical solvers, while highlighting
challenges related to training efficiency and stability.