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Artificial Neural Network Methods in Quantum Mechanics
I. E. Lagaris, A. Likas, D. I. Fotiadis
abstract: 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 Schr\"odinger equation for the Morse
potential that has an analytically known solution, to test the accuracy of the
method. We then proceed with the Schr\"odinger and the Dirac equations for a
muonic atom, as well as with a non-local Schr\"odinger 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 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9705029
- categories:
- quant-ph comp-gas nlin.CG physics.comp-ph
- comments:
- Latex file, 29pages, 11 psfigs, submitted in CPC
- doi:
- 10.1016/S0010-4655(97)00054-4
- arxiv_id:
- quant-ph/9705029
- journal_ref:
- Comput.Phys.Commun. 104 (1997) 1-14
- created:
- 1997-05-15
Full article ▸
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