Representation of Quantum States of Two-Dimensional simple Harmonic oscillator by convolution Neural Network

摘要

It is proposed to train a deep convolution neural network (CNN) to learn the mapping relation between two-dimensional electrostatic potential and ground state energy eigenvalue by using the feature extraction and function fitting ability of machine learning (ML), so as to avoid the difficulty of strict solution of Schrodinger equation. The potential energy function is processed by CNN image processing, and the projection of the two-dimensional simple harmonic oscillator potential energy function on the two-dimensional plane is taken as input. Experimental results verify the validity of the method: the average absolute error is 0.0372eV, The Standard Deviation was 0.429eV, and the Relative Error was 1.042%.