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

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.