Physics-Informed Neural Networks for Quantum Wavefunctions

The wave functions and permitted energy levels of quantum systems, which characterize the probability distributions and particle behaviors, are able to be determined via the time-independent Schrodinger equation. Our research study introduces an experimental method of solving the time-independent Schrodinger equation by utilizing Physics-Informed Neural Networks (PINNs) with a customized loss function designed for output waveshape prediction. The technique makes use of PINNs' capacity to directly integrate physical rules into the learning process, assuring that the solutions follow the guiding principles of quantum mechanics. We forecast the associated wavefunctions for different energy levels (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> states) and effectively solve the Schrodinger equation for distinct quantum states by using PINNs and a customized loss function. Our findings show that PINNs are a reliable and accurate way to represent the fine features of quantum wavefunctions, and they present a viable substitute for more conventional numerical techniques. This methodology not only improves computer performance but also offers more profound understanding of the behavior of systems in quantum mechanics, which may have implications for material science, nanotechnology, and quantum computing.