Physics-Informed Classical and Quantum Neural Networks for One-Dimensional Schrodinger Eigenvalue Problems

Quantum Physics arXiv:2609.22189 (quant-ph) [Submitted on 28 Aug 2026] Title:Physics-Informed Classical and Quantum Neural Networks for One-Dimensional Schrodinger Eigenvalue Problems Authors:Tariq Mahmood, Waqas Arshad, Bilal Naseer, Alfredo Raya View a PDF of the paper titled Physics-Informed Classical and Quantum Neural Networks for One-Dimensional Schrodinger Eigenvalue Problems, by Tariq Mahmood and 3 other authors View PDF HTML (experimental) Abstract:The Schrodinger equation in one spatial dimension admits a small set of exactly solvable potentials that serve as natural proving grounds for any new eigenvalue solver. We formulate Physics-Informed Neural Networks (PINNs) and Physics-Informed Quantum Neural Networks (PIQNNs) for the time-independent Schrodinger equation and apply them to three of these benchmarks: the harmonic oscillator, the infinite square well, and the finite square well. In each case a composite loss encodes the differential-equation residual, the normalization condition, the boundary behavior, and the orthogonality between eigenstates, so that the trial wave function is driven toward a genuine eigenfunction without supervised data. The eigenvalues and wave functions returned by both methods are compared against the exact spectra and against three classical references: the matrix Numerov method, the finite difference method, and the shooting method. For the smooth oscillator the two neural solvers reproduce the lowest four eigenvalues to parts per million, while for the square wells they recover the analytic levels with comparable fidelity even where the potential is discontinuous. The quantum circuit, built as a layered angle-embedding ansatz with strongly entangling blocks, converges more reliably than its classical counterpart on the higher excited states, where the loss landscape of the classical network becomes harder to navigate. Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2609.22189 [quant-ph] (or arXiv:2609.22189v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.22189 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tariq Mahmood [view email] [v1] Fri, 28 Aug 2026 19:41:40 UTC (595 KB) Full-text links: Access Paper: View a PDF of the paper titled Physics-Informed Classical and Quantum Neural Networks for One-Dimensional Schrodinger Eigenvalue Problems, by Tariq Mahmood and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cs cs.LG hep-ph hep-th References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)