Artificial neural network methods in quantum mechanics

✍ Scribed by I.E. Lagaris; A. Likas; D.I. Fotiadis

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 829 KB
• Volume: 104
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/s0010-4655(97)00054-4

✦ Synopsis

In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrodinger equation for the Morse potential that has an analytically known solution, to test the accuracy of the method. We then proceed with the Schr6dinger and the Dirac equations for a muonic atom, as well as with a nonlocal Schrijdinger integrodifferential equation that models the n + a system in the framework of the resonating group method. In two dimensions we consider the well-studied Henon-Heiles Hamiltonian and in three dimensions the model problem of three coupled anharmonic oscillators. The method in all of the treated cases proved to be highly accurate, robust and efficient. Hence it is a promising tool for tackling problems of higher complexity and dimensionality. @ 1997 Elsevier Science B.V.