engleski

Numerical Solution of the Schrödinger Equation Using a Neural Network Approach

This paper overviews the solution of the Schrödinger equation for the case of one-dimensional infinite potential well with a neural network approach. Using a single hidden layer neural network, which is proved to be a universal function approximator, and by exploiting the automatic differentiation capabilities, it is possible to achieve very accurate values of the wave function and eigenvalues of the ground state. The loss function with integrated physical knowledge is set up as an unconstrained nonlinear problem and parameters of a neural network are being learnt in a completely unsupervised manner. Such a technique could potentially serve as a door opener for solving high-dimensional quantum mechanics problems, otherwise tedious to set up for standard mesh-based numerical methods.

neural network ; unsupervised learning ; automatic differentiation ; eigenvalue problem ; Schrördinger equation

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