Theoretical Study On Resonant States Of One-Electron Atoms Under Screened Coulomb Potential

The problem of atomic resonance states under screened Coulomb potentials has been studied for a long time in different research fields of physics.In the early days,this kind of work was mainly concentrated in metals,semiconductors and other solid-state systems.In recent years,it is also often used in problems such as quantum plasmas research.The three common screened Coulomb potentials include screened Coulomb potential,exponential cosine screened Coulomb potential,and Hulthén potential.This paper mainly research the problem of resonance states of one-electron atoms under Hulthén potential.The Hulthén potential is a short-range spherical Coulomb potential.It has very important research significance in many fields of physics,such as nuclear physics and particle physics,atomic and molecular physics,and condensed matter physics.It has been obtained in relativity and non-relativistic quantum mechanics.extensive research.The Hulthén potential is expression asV_HP=-Zλe^-λr/1-e^-λrIn the past few decades,researchers have tried to find the energy eigenvalues and eigenfunctions of the Hulthén potential.Since the wave function contains all the necessary information about the quantum system under consideration,it is very important to solve the Hulthén potential and the Schr（?）dinger equation accurately.However,except for the case of s-states,the Hulthén potential cannot be solved analytically.But there are many ways to study its scattering and bound states.Many phenomena in physics are simulated by linear and nonlinear differential equations,many of them cannot be solved analytically,so numerical methods are need to solve these equations,so it is very important to find efficient methods to solve the related differential equations.Spectral method is a kind of effective method for solving differential equations,and pseudospectral method is closely related to spectral method,and it is a numerical analysis method for solving partial differential equations in applied mathematics and computing science.Pseudospectral basis functions can be represented on a discrete grid,are used in the basis function of the spectral method.This approach simplifies the calculation of some operators,which can speed up the calculation when using fast algorithms.The generalized pseudospectral method is always based on the configuration method of the global method,this method can produce very reliable results in important systems such as confined quantum systems.However,for single-electron atomic systems,calculations using the generalized pseudospectral method have great advantages.We need to use the generalized pseudospectral method to solve the non-relativistic radial Schr（?）dinger equation for single-electron systems to study the problem of p-state wave resonance.In atomic,molecular,and nuclear physics,the complex coordinate rotation method is a widely used theoretical tool for studying resonance states.Resonance states play important roles in atomic,molecular,and nuclear physics.In this paper,the complex coordinate rotation method is used to solve the energy spectrum,by performing the transformationr→re ^iθ.Thisθhas two characteristics（1）The bound state remains unchanged no matter how large rotation angle is employed;（2）The continuous spectra can be clockwise rotated by 2θ.（3）Resonances are rotated into the fourth quadrant,after that these resonances form a new cut line and do not change withθ.The energy of the bound state does not change with the change of the rotation angle,but the continuous state changes with the change of the rotation angle,so that the resonance state is exposed from the continuous state.Resonance points are plotted on the complex energy plane associated with the Hulthén potential.In this paper,it is necessary to combine the generalized pseudospectral method with the complex coordinate rotation method to study the p-state wave resonance of single-electron atoms under the Hulthén potential,and find the information we want from the obtained data.The combination of these two methods provides resonance energies and widths with very high accuracy.