dorsal/arxiv
View SchemaArtificial Neural Network Methods in Quantum Mechanics
| Authors | I. E. Lagaris, A. Likas, D. I. Fotiadis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9705029 |
| URL | https://arxiv.org/abs/quant-ph/9705029 |
| DOI | 10.1016/S0010-4655(97)00054-4 |
| Journal | Comput.Phys.Commun. 104 (1997) 1-14 |
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.
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"abstract": "In a previous article we have shown how one can employ Artificial Neural\nNetworks (ANNs) in order to solve non-homogeneous ordinary and partial\ndifferential equations. In the present work we consider the solution of\neigenvalue problems for differential and integrodifferential operators, using\nANNs. We start by considering the Schr\\\"odinger equation for the Morse\npotential that has an analytically known solution, to test the accuracy of the\nmethod. We then proceed with the Schr\\\"odinger and the Dirac equations for a\nmuonic atom, as well as with a non-local Schr\\\"odinger integrodifferential\nequation that models the $n+\\alpha$ system in the framework of the resonating\ngroup method. In two dimensions we consider the well studied Henon-Heiles\nHamiltonian and in three dimensions the model problem of three coupled\nanharmonic oscillators. The method in all of the treated cases proved to be\nhighly accurate, robust and efficient. Hence it is a promising tool for\ntackling problems of higher complexity and dimensionality.",
"arxiv_id": "quant-ph/9705029",
"authors": [
"I. E. Lagaris",
"A. Likas",
"D. I. Fotiadis"
],
"categories": [
"quant-ph",
"comp-gas",
"nlin.CG",
"physics.comp-ph"
],
"doi": "10.1016/S0010-4655(97)00054-4",
"journal_ref": "Comput.Phys.Commun. 104 (1997) 1-14",
"title": "Artificial Neural Network Methods in Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/9705029"
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