Unsupervised Neural Networks for Quantum Eigenvalue Problems

Henry Jin; Marios Mattheakis; Pavlos Protopapas

Unsupervised Neural Networks for Quantum Eigenvalue Problems

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arxiv 2010.05075 v1 pith:FEGTCIP5 submitted 2020-10-10 physics.comp-ph cs.LG

Henry Jin , Marios Mattheakis , Pavlos Protopapas This is my paper · ORCID

classification physics.comp-phcs.LG

keywords eigenvalueproblemsquantumunsupervisedmethodnetworkneuralsolutions

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Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that identically satisfy the boundary conditions. A scanning mechanism is embedded allowing the method to find an arbitrary number of solutions. The network optimization is data-free and depends solely on the predictions. The unsupervised method is used to solve the quantum infinite well and quantum oscillator eigenvalue problems.

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