Application Of Convolution Neural Network In The Expression Of Quantum States

The traditional meth od of solving quantum mechanics is to get the concrete form of the wave function by the second order partial differential equation,and then calculate the properties of the microscopic particles.The number of orthogonal bases,that is,the dimension of Hilbert space,will increase exponentially by the expansion of wave functions,which makes it difficult to solve the wave functions.With the rapid development of artificial intelligence and graphics processor GPU,machine learning methods are emerging in various fields.Therefore,it is a novel and meaningful problem to explore the application of machine learning technology in solving quantum mechanics problems.Convolution neural network belongs to supervised learning and needs a lot of exact solutions to train CNN model.Because there are one.-to-one corresponding analytical solutions between the potential function of hydrogen atom and the energy eigenvalues,the application of machine learning in quantum state representation is studied in this paper,taking the harmonic oscillator and hydrogen atom as examples.The projection of the potential function of the harmonic oscillator and hydrogen atom on the two-dimensional plane is a plane image.The analytical solution is used as a label to evaluate the accuracy of the energy eigenvalues predicted by CNN.The two-dimensional images and labels of potential functions of multiple harmonic oscillators and hydrogen atoms can be used as input training CNN model,and the mapping relationship between harmonic subpotential function and the eigenvalues of ground state energy can be obtained by using CNN to process the images.And the mapping relationship between the hydrogen atom potential function and the energy eigenvalues of the ground state,the first excited state and the second excited state.The trained CNN model can predict the ground state energy of different harmonic oscillator,the ground state of different hydrogen atom,the first excited state and the second excited state energy without Schrodinger equation.Therefore,four sample image data sets of 224×224 are constructed on MATLAB.The VGG network model is improved on the TensorFlow deep learning platform.The improved 18-layer Bright VGG network model is used to train the data samples,and the mapping between the two-dimensional potential function and the energy eigenvalues is established.The average absolute error of the ground state prediction of different harmonic oscillator is improved from 0.0427eV to 0.0372eV,the relative error is improved from 0.566eV to 0.429eV,and the standard deviation is improved from 1.233%to 1.042%by the Bright VGG network model.Through the comparison,the accuracy and reliability of the Bright VGG network built in this paper are explained.At the same time,the trained CNN model can accurately predict the quantum states of the harmonic oscillator and hydrogen atom.The experimental results verify the effectiveness of the CNN method proposed in this paper to express the quantum states.