An Optimization Method For Finding Bose-Einstein Ground State Solution

In recent years,a series of important achievements have been made in experimental studies on the ground state solutions of Bose-Einstein condensation.Based on these related research results,this thesis first uses dimension reduction and nondimensionalization methods to transform the problem of the ground state solutions of Bose-Einstein condensation into an energy functional extremization problem.When discretizing the functional,finite difference method,Fourier spectral method,and Legendre spectral method are used to discretize the one-dimensional and two-dimensional cases of the energy functional,respectively.Secondly,this thesis uses a highly efficient numerical optimization algorithm,namely the sequential quadratic programming(SQP)method,to solve the problem of the ground state solutions of Bose-Einstein condensation.This optimization algorithm is applied to process the one-dimensional and two-dimensional energy functional extremum problems respectively.Finally,appropriate numerical examples are selected for numerical simulation experiments.through analyzing the experimental data and images,we have verified the reliability and effectiveness of the optimization method in solving the ground state of the Bose-Einstein condensation problem.