Artificial Neural Network methods in quantum mechanics
Artificial Neural Network methods in quantum mechanics
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DOI：
10.1016/s0010-4655(97)00054-4
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发表时间：
1997-08-01
影响因子：
6.3
通讯作者：
Fotiadis, DI
中科院分区：
文献类型：
--
作者：
Lagaris, IE;Likas, A;Fotiadis, DI
在之前的文章中，我们已经展示了如何使用人工神经网络（ann）来解决非齐次常微分方程和偏微分方程。在本工作中，我们考虑使用ann来解决微分算子和积分微分算子的特征值问题。我们首先考虑具有解析解的莫尔斯势的薛定谔方程，以测试该方法的准确性，然后我们继续考虑介子原子的薛定谔和狄拉克方程，以及在谐振群方法框架下模拟n + α系统的非局部薛定谔积分微分方程。在二维中，我们考虑了已经得到充分研究的Henon-Heiles哈密顿量，在三维中，我们考虑了三个耦合非谐振子的模型问题，在所有处理的情况下，该方法都证明了它是高度精确、鲁棒和高效的。因此，它是解决更高复杂性和维度问题的一个很有前途的工具。(C) 1997爱思唯尔科学有限公司
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 Schrodinger and the Dirac equations for a muonic atom, as well as with a nonlocal Schrodinger 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. (C) 1997 Elsevier Science B.V.