TY - JOUR

T1 - Numerical solution of the Schrödinger equation by neural network and genetic algorithm

AU - Sugawara, M.

N1 - Funding Information:
This work is supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture and, in part, by “Research and Development Applying Advanced Computational Science and Technology” of Japan Science and Technology Corporation. Authors are grateful to Dr. D.L. Carroll for his Fortran GA driver, which is open to the public on the Internet.

PY - 2001/11/1

Y1 - 2001/11/1

N2 - A new approach for solving the Schrödinger equation based on genetic algorithm (GA) and artificial neural network (NN) is presented. Feed-forward perceptron-type network is used to represent the wavefunction, while network parameters are optimized by micro-genetic algorithm so that the NN satisfies the Schrödinger equation. In the GA breeding process, random point evaluation method (RPEM) for fitness evaluation is introduced to improve the convergence. Final solution is obtained by invoking deterministic optimizer which corresponds to a "learning process" of the NN. The present method is tested in the calculation of one-dimensional harmonic oscillator and other model potentials.

AB - A new approach for solving the Schrödinger equation based on genetic algorithm (GA) and artificial neural network (NN) is presented. Feed-forward perceptron-type network is used to represent the wavefunction, while network parameters are optimized by micro-genetic algorithm so that the NN satisfies the Schrödinger equation. In the GA breeding process, random point evaluation method (RPEM) for fitness evaluation is introduced to improve the convergence. Final solution is obtained by invoking deterministic optimizer which corresponds to a "learning process" of the NN. The present method is tested in the calculation of one-dimensional harmonic oscillator and other model potentials.

KW - Eigenvalue problems

KW - Genetic Algorithm

KW - Neural network

KW - Schrödinger equation

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U2 - 10.1016/S0010-4655(01)00286-7

DO - 10.1016/S0010-4655(01)00286-7

M3 - Article

AN - SCOPUS:0035501084

SN - 0010-4655

VL - 140

SP - 366

EP - 380

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 3

ER -