| The Kapitza-Dirac effect has been widely studied since it was proposed.The standing wave potential field is usually treated as plane wave superposition in previous studies.In this paper,Gaussian light is introduced as a standing wave potential field,and its longitudinal component is considered.The second order time-dependent perturbation theory is used for numerical calculation to solve the probability of electron spin states,and the fine influence of the longitudinal component of Gaussian light potential field on electron spin is obtained.This paper describes the external field interacting with electrons in more detail.The wave amplitudes used are obtained from the Fourier transform of the vector field.we have investigated the performance and computation accuracy of a relativistic quantum mechanical time-propagation method based on time-dependent perturbation theory.We conclude from our simulation that for computing Kapitza-Dirac scattering with a Gaussian beam potential there is no numerical convergence of the resulting diffraction pattern.More precisely,the final computation result depends partially on the resolution of the grid along the laser beam propagation direction,which is a purely numerical quantity.Therefore,the simulated quantum dynamics of the specific scenario with our method cannot be associated with a physically valid quantity.Still,within the context of our calculations,we find that an influence of the Gaussian beam’s longitudinal polarization has a negligible small influence on the spin dynamics and the diffraction pattern of the effect. |
