ARTIFICIAL NEURAL-NETWORK METHODS IN QUANTUM-MECHANICS

In a previous article we have shown how one can employ Artificial Neur al Networks (ANNs) in order to solve non-homogeneous ordinary and part ial differential equations, In the present work we consider the soluti on of eigenvalue problems for differential and integrodifferential ope rators, using ANNs. We start by considering the Schrodinger equation f or the Morse potential that has an analytically known solution, to tes t the accuracy of the method, We then proceed with the Schrodinger and the Dirac equations for a muonic atom, as well as with a nonlocal Sch rodinger integrodifferential equation that models the n + alpha system in the framework of the resonating group method, In two dimensions we consider the well-studied Henon-Heiles Hamiltonian and in three dimen sions the model problem of three coupled anharmonic oscillators, The m ethod 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. (C) 1997 Elsevier Science B.V.