| The Compton profile reveals the electron momentum density distribution of atoms and molecules,especially sensitive to the change of valence electron wave function.Accurate Compton profile can not only help us understand the electronic structure of atoms and molecules,but also can be used as a benchmark to test the target electron wave functions obtained by various theoretical models and calculation methods.In this paper,the pseudospectral-fitting(PSF)method is proposed to obtain the radial wave function in the position space,and it is proved to be equivalent to the analytical solution.Then the radial wave function in the momentum space is calculated in series form analytically,thus avoiding the numerical difficulty in high oscillation integral.Finally,the high-accuracy Compton profile with sufficient effective number of bits at any momentum is calculated by Gauss-Legendre integral.In Chapter 1,we briefly introduce the research progress of Compton profile in last decades.In Chapter 2,the pseudospectral method is used to solve the stationary Schr(?)dinger equation and the algorithm for calculating the Compton profile are introduced in detail.In Chapter 3,the eigenenergy and wave function of hydrogen-like ions are solved based on the pseudospectral method,which are compared with the analytical results.The results show that the wave function solved by the pseudospectral method does not have global accuracy.Therefore,this paper proposes the idea of achieving the globally exact wave function by using the least-square method.Finally,the high-accuracy Compton profile of hydrogen-like ions is given by Gauss-Legendre integral.In the previous calculation,the accuracy is dependent on the density of grid points very much.However,with the increase of grid points,the time-consuming is more,and the improvement of accuracy is not significant.The algorithm used in this paper not only avoids the cliff phenomenon when the upper limit of integration is truncated,but also greatly improves the computational efficiency and is suitable for a considerable range of momentum.The calculation result has sufficient significant digits.The fourth chapter is the summary and outlook. |
