Unsupervised Neural Networks for Quantum Eigenvalue Problems
This work addresses eigenvalue problems in quantum physics using a novel neural network approach, but it appears incremental as it builds on existing unsupervised methods for specific quantum systems.
The authors tackled the problem of solving differential eigenvalue problems in quantum mechanics by developing an unsupervised neural network that discovers eigenfunctions and eigenvalues without data, applying it to quantum infinite well and oscillator problems with solutions that satisfy boundary conditions.
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.