ua nt - p h / 97 05 02 9 v 1 1 5 M ay 1 99 7 Artificial Neural Network Methods in Quantum Mechanics

In a previous article [1] we have shown how one can employ Artificial Neu-ral Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigen-value problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrödinger equation for the Morse potential that has an analytically known solution, to test the accuracy of the method. We then proceed with the Schrödinger and the Dirac equations for a muonic atom, as well as with a non-local Schrödinger integrodifferential equation that models the n + α system in the framework of the resonating group method. In two dimensions we consider the well studied [2] 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.